id	sid	tid	token	lemma	pos
ejpam-2346	1	1	compile	compile	NOUN
ejpam-2346	1	2	/	/	SYM
ejpam-2346	1	3	output.dvi	output.dvi	NOUN
ejpam-2346	1	4	european	european	ADJ
ejpam-2346	1	5	journal	journal	NOUN
ejpam-2346	1	6	of	of	ADP
ejpam-2346	1	7	pure	pure	ADJ
ejpam-2346	1	8	and	and	CCONJ
ejpam-2346	1	9	applied	apply	VERB
ejpam-2346	1	10	mathematics	mathematic	NOUN
ejpam-2346	1	11	vol	vol	NOUN
ejpam-2346	1	12	.	.	PUNCT
ejpam-2346	2	1	11	11	NUM
ejpam-2346	2	2	,	,	PUNCT
ejpam-2346	2	3	no	no	INTJ
ejpam-2346	2	4	.	.	NOUN
ejpam-2346	2	5	1	1	NUM
ejpam-2346	2	6	,	,	PUNCT
ejpam-2346	2	7	2018	2018	NUM
ejpam-2346	2	8	,	,	PUNCT
ejpam-2346	2	9	315	315	NUM
ejpam-2346	2	10	-	-	SYM
ejpam-2346	2	11	330	330	NUM
ejpam-2346	2	12	issn	issn	PROPN
ejpam-2346	2	13	1307	1307	NUM
ejpam-2346	2	14	-	-	SYM
ejpam-2346	2	15	5543	5543	NUM
ejpam-2346	2	16	–	–	PUNCT
ejpam-2346	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2346	2	18	published	publish	VERB
ejpam-2346	2	19	by	by	ADP
ejpam-2346	2	20	new	new	PROPN
ejpam-2346	2	21	york	york	PROPN
ejpam-2346	2	22	business	business	PROPN
ejpam-2346	2	23	global	global	ADJ
ejpam-2346	2	24	regularization	regularization	NOUN
ejpam-2346	2	25	of	of	ADP
ejpam-2346	2	26	heptahedra	heptahedra	NOUN
ejpam-2346	2	27	using	use	VERB
ejpam-2346	2	28	geometric	geometric	ADJ
ejpam-2346	2	29	element	element	NOUN
ejpam-2346	2	30	transformation	transformation	NOUN
ejpam-2346	2	31	method	method	NOUN
ejpam-2346	2	32	santu	santu	PROPN
ejpam-2346	2	33	dey1	dey1	PROPN
ejpam-2346	2	34	,	,	PUNCT
ejpam-2346	2	35	budhhadev	budhhadev	PROPN
ejpam-2346	2	36	pal	pal	PROPN
ejpam-2346	2	37	2,∗	2,∗	NUM
ejpam-2346	2	38	,	,	PUNCT
ejpam-2346	2	39	arindam	arindam	PROPN
ejpam-2346	2	40	bhattacharyya1	bhattacharyya1	PROPN
ejpam-2346	2	41	1	1	NUM
ejpam-2346	2	42	department	department	NOUN
ejpam-2346	2	43	of	of	ADP
ejpam-2346	2	44	mathematics	mathematic	NOUN
ejpam-2346	2	45	,	,	PUNCT
ejpam-2346	2	46	jadavpur	jadavpur	PROPN
ejpam-2346	2	47	university	university	PROPN
ejpam-2346	2	48	,	,	PUNCT
ejpam-2346	2	49	kolkata-700032	kolkata-700032	INTJ
ejpam-2346	2	50	,	,	PUNCT
ejpam-2346	2	51	india	india	PROPN
ejpam-2346	2	52	2	2	PROPN
ejpam-2346	2	53	institute	institute	PROPN
ejpam-2346	2	54	of	of	ADP
ejpam-2346	2	55	science	science	PROPN
ejpam-2346	2	56	,	,	PUNCT
ejpam-2346	2	57	department	department	NOUN
ejpam-2346	2	58	of	of	ADP
ejpam-2346	2	59	mathematics	mathematics	PROPN
ejpam-2346	2	60	,	,	PUNCT
ejpam-2346	2	61	banaras	banaras	PROPN
ejpam-2346	2	62	hindu	hindu	PROPN
ejpam-2346	2	63	university	university	PROPN
ejpam-2346	2	64	,	,	PUNCT
ejpam-2346	2	65	varanasi	varanasi	PROPN
ejpam-2346	2	66	,	,	PUNCT
ejpam-2346	2	67	uttar	uttar	PROPN
ejpam-2346	2	68	pradesh	pradesh	PROPN
ejpam-2346	2	69	221005	221005	NUM
ejpam-2346	2	70	,	,	PUNCT
ejpam-2346	2	71	india	india	PROPN
ejpam-2346	2	72	abstract	abstract	NOUN
ejpam-2346	2	73	.	.	PUNCT
ejpam-2346	3	1	by	by	ADP
ejpam-2346	3	2	geometric	geometric	ADJ
ejpam-2346	3	3	element	element	NOUN
ejpam-2346	3	4	transformation	transformation	NOUN
ejpam-2346	3	5	method	method	NOUN
ejpam-2346	3	6	(	(	PUNCT
ejpam-2346	3	7	getme	getme	NOUN
ejpam-2346	3	8	)	)	PUNCT
ejpam-2346	3	9	always	always	ADV
ejpam-2346	3	10	we	we	PRON
ejpam-2346	3	11	get	get	VERB
ejpam-2346	3	12	a	a	DET
ejpam-2346	3	13	new	new	ADJ
ejpam-2346	3	14	element	element	NOUN
ejpam-2346	3	15	.	.	PUNCT
ejpam-2346	4	1	in	in	ADP
ejpam-2346	4	2	this	this	DET
ejpam-2346	4	3	paper	paper	NOUN
ejpam-2346	4	4	,	,	PUNCT
ejpam-2346	4	5	we	we	PRON
ejpam-2346	4	6	investigate	investigate	VERB
ejpam-2346	4	7	the	the	DET
ejpam-2346	4	8	regularization	regularization	NOUN
ejpam-2346	4	9	of	of	ADP
ejpam-2346	4	10	heptahedra	heptahedra	PROPN
ejpam-2346	4	11	using	use	VERB
ejpam-2346	4	12	getme	getme	NOUN
ejpam-2346	4	13	.	.	PUNCT
ejpam-2346	5	1	energy	energy	NOUN
ejpam-2346	5	2	function	function	NOUN
ejpam-2346	5	3	is	be	AUX
ejpam-2346	5	4	a	a	DET
ejpam-2346	5	5	cost	cost	NOUN
ejpam-2346	5	6	function	function	NOUN
ejpam-2346	5	7	for	for	ADP
ejpam-2346	5	8	heptahedra	heptahedra	NOUN
ejpam-2346	5	9	which	which	PRON
ejpam-2346	5	10	is	be	AUX
ejpam-2346	5	11	also	also	ADV
ejpam-2346	5	12	applicable	applicable	ADJ
ejpam-2346	5	13	for	for	ADP
ejpam-2346	5	14	octahedra	octahedron	NOUN
ejpam-2346	5	15	,	,	PUNCT
ejpam-2346	5	16	decahedra	decahedra	NOUN
ejpam-2346	5	17	,	,	PUNCT
ejpam-2346	5	18	hexahedra	hexahedra	PROPN
ejpam-2346	5	19	etc	etc	X
ejpam-2346	5	20	.	.	X
ejpam-2346	5	21	is	be	AUX
ejpam-2346	5	22	defined	define	VERB
ejpam-2346	5	23	by	by	ADP
ejpam-2346	5	24	a	a	DET
ejpam-2346	5	25	particular	particular	ADJ
ejpam-2346	5	26	process	process	NOUN
ejpam-2346	5	27	,	,	PUNCT
ejpam-2346	5	28	which	which	PRON
ejpam-2346	5	29	we	we	PRON
ejpam-2346	5	30	call	call	VERB
ejpam-2346	5	31	base	base	ADJ
ejpam-2346	5	32	diagonal	diagonal	ADJ
ejpam-2346	5	33	apex	apex	NOUN
ejpam-2346	5	34	method	method	NOUN
ejpam-2346	5	35	(	(	PUNCT
ejpam-2346	5	36	bdame	bdame	PROPN
ejpam-2346	5	37	)	)	PUNCT
ejpam-2346	5	38	.	.	PUNCT
ejpam-2346	6	1	we	we	PRON
ejpam-2346	6	2	also	also	ADV
ejpam-2346	6	3	try	try	VERB
ejpam-2346	6	4	to	to	PART
ejpam-2346	6	5	find	find	VERB
ejpam-2346	6	6	the	the	DET
ejpam-2346	6	7	characterization	characterization	NOUN
ejpam-2346	6	8	of	of	ADP
ejpam-2346	6	9	different	different	ADJ
ejpam-2346	6	10	cost	cost	NOUN
ejpam-2346	6	11	function	function	NOUN
ejpam-2346	6	12	using	use	VERB
ejpam-2346	6	13	bdame	bdame	NOUN
ejpam-2346	6	14	when	when	SCONJ
ejpam-2346	6	15	we	we	PRON
ejpam-2346	6	16	transform	transform	VERB
ejpam-2346	6	17	a	a	DET
ejpam-2346	6	18	heptahedra	heptahedra	NOUN
ejpam-2346	6	19	by	by	ADP
ejpam-2346	6	20	getme	getme	NOUN
ejpam-2346	6	21	.	.	PUNCT
ejpam-2346	7	1	2010	2010	NUM
ejpam-2346	7	2	mathematics	mathematic	NOUN
ejpam-2346	7	3	subject	subject	NOUN
ejpam-2346	7	4	classifications	classification	NOUN
ejpam-2346	7	5	:	:	PUNCT
ejpam-2346	7	6	65m50	65m50	NUM
ejpam-2346	7	7	,	,	PUNCT
ejpam-2346	7	8	51m04	51m04	NUM
ejpam-2346	7	9	.	.	PUNCT
ejpam-2346	8	1	key	key	ADJ
ejpam-2346	8	2	words	word	NOUN
ejpam-2346	8	3	and	and	CCONJ
ejpam-2346	8	4	phrases	phrase	NOUN
ejpam-2346	8	5	:	:	PUNCT
ejpam-2346	8	6	heptahedron	heptahedron	NOUN
ejpam-2346	8	7	,	,	PUNCT
ejpam-2346	8	8	mesh	mesh	NOUN
ejpam-2346	8	9	quality	quality	NOUN
ejpam-2346	8	10	,	,	PUNCT
ejpam-2346	8	11	iterative	iterative	NOUN
ejpam-2346	8	12	method	method	NOUN
ejpam-2346	8	13	,	,	PUNCT
ejpam-2346	8	14	regularization	regularization	NOUN
ejpam-2346	8	15	,	,	PUNCT
ejpam-2346	8	16	finite	finite	PROPN
ejpam-2346	8	17	element	element	NOUN
ejpam-2346	8	18	mesh	mesh	NOUN
ejpam-2346	8	19	,	,	PUNCT
ejpam-2346	8	20	cost	cost	NOUN
ejpam-2346	8	21	functions	function	NOUN
ejpam-2346	8	22	.	.	PUNCT
ejpam-2346	9	1	1	1	X
ejpam-2346	9	2	.	.	X
ejpam-2346	9	3	introduction	introduction	NOUN
ejpam-2346	9	4	in	in	ADP
ejpam-2346	9	5	many	many	ADJ
ejpam-2346	9	6	finite	finite	ADJ
ejpam-2346	9	7	element	element	NOUN
ejpam-2346	9	8	applications	application	NOUN
ejpam-2346	9	9	unstructured	unstructure	VERB
ejpam-2346	9	10	tessellations	tessellation	NOUN
ejpam-2346	9	11	of	of	ADP
ejpam-2346	9	12	the	the	DET
ejpam-2346	9	13	geometry	geometry	NOUN
ejpam-2346	9	14	under	under	ADP
ejpam-2346	9	15	consideration	consideration	NOUN
ejpam-2346	9	16	play	play	VERB
ejpam-2346	9	17	a	a	DET
ejpam-2346	9	18	fundamental	fundamental	ADJ
ejpam-2346	9	19	role	role	NOUN
ejpam-2346	9	20	.	.	PUNCT
ejpam-2346	10	1	therefore	therefore	ADV
ejpam-2346	10	2	,	,	PUNCT
ejpam-2346	10	3	the	the	DET
ejpam-2346	10	4	generation	generation	NOUN
ejpam-2346	10	5	of	of	ADP
ejpam-2346	10	6	quality	quality	NOUN
ejpam-2346	10	7	meshes	mesh	NOUN
ejpam-2346	10	8	are	be	AUX
ejpam-2346	10	9	essential	essential	ADJ
ejpam-2346	10	10	steps	step	NOUN
ejpam-2346	10	11	of	of	ADP
ejpam-2346	10	12	the	the	DET
ejpam-2346	10	13	simulation	simulation	NOUN
ejpam-2346	10	14	process	process	NOUN
ejpam-2346	10	15	,	,	PUNCT
ejpam-2346	10	16	since	since	SCONJ
ejpam-2346	10	17	mesh	mesh	NOUN
ejpam-2346	10	18	quality	quality	NOUN
ejpam-2346	10	19	has	have	VERB
ejpam-2346	10	20	an	an	DET
ejpam-2346	10	21	impact	impact	NOUN
ejpam-2346	10	22	on	on	ADP
ejpam-2346	10	23	solution	solution	NOUN
ejpam-2346	10	24	accuracy	accuracy	NOUN
ejpam-2346	10	25	and	and	CCONJ
ejpam-2346	10	26	the	the	DET
ejpam-2346	10	27	efficiency	efficiency	NOUN
ejpam-2346	10	28	of	of	ADP
ejpam-2346	10	29	the	the	DET
ejpam-2346	10	30	computational	computational	ADJ
ejpam-2346	10	31	methods	method	NOUN
ejpam-2346	10	32	involved	involve	VERB
ejpam-2346	10	33	[	[	PUNCT
ejpam-2346	10	34	1	1	NUM
ejpam-2346	10	35	,	,	PUNCT
ejpam-2346	10	36	2	2	NUM
ejpam-2346	10	37	,	,	PUNCT
ejpam-2346	10	38	6	6	NUM
ejpam-2346	10	39	,	,	PUNCT
ejpam-2346	10	40	9	9	NUM
ejpam-2346	10	41	]	]	PUNCT
ejpam-2346	10	42	.	.	PUNCT
ejpam-2346	11	1	in	in	ADP
ejpam-2346	11	2	[	[	X
ejpam-2346	11	3	11	11	NUM
ejpam-2346	11	4	]	]	PUNCT
ejpam-2346	11	5	,	,	PUNCT
ejpam-2346	11	6	geometric	geometric	ADJ
ejpam-2346	11	7	element	element	NOUN
ejpam-2346	11	8	transformation	transformation	NOUN
ejpam-2346	11	9	method	method	NOUN
ejpam-2346	11	10	(	(	PUNCT
ejpam-2346	11	11	getme	getme	NOUN
ejpam-2346	11	12	)	)	PUNCT
ejpam-2346	11	13	is	be	AUX
ejpam-2346	11	14	represented	represent	VERB
ejpam-2346	11	15	as	as	ADP
ejpam-2346	11	16	a	a	DET
ejpam-2346	11	17	simple	simple	ADJ
ejpam-2346	11	18	geometric	geometric	ADJ
ejpam-2346	11	19	operation	operation	NOUN
ejpam-2346	11	20	.	.	PUNCT
ejpam-2346	12	1	the	the	DET
ejpam-2346	12	2	effect	effect	NOUN
ejpam-2346	12	3	of	of	ADP
ejpam-2346	12	4	this	this	DET
ejpam-2346	12	5	transformation	transformation	NOUN
ejpam-2346	12	6	,	,	PUNCT
ejpam-2346	12	7	if	if	SCONJ
ejpam-2346	12	8	applied	apply	VERB
ejpam-2346	12	9	iteratively	iteratively	ADV
ejpam-2346	12	10	,	,	PUNCT
ejpam-2346	12	11	gives	give	VERB
ejpam-2346	12	12	asymptotical	asymptotical	ADJ
ejpam-2346	12	13	but	but	CCONJ
ejpam-2346	12	14	rapid	rapid	ADJ
ejpam-2346	12	15	regularization	regularization	NOUN
ejpam-2346	12	16	of	of	ADP
ejpam-2346	12	17	the	the	DET
ejpam-2346	12	18	initial	initial	ADJ
ejpam-2346	12	19	element	element	NOUN
ejpam-2346	12	20	.	.	PUNCT
ejpam-2346	13	1	the	the	DET
ejpam-2346	13	2	authors	author	NOUN
ejpam-2346	13	3	of	of	ADP
ejpam-2346	13	4	[	[	X
ejpam-2346	13	5	11	11	NUM
ejpam-2346	13	6	]	]	PUNCT
ejpam-2346	13	7	have	have	AUX
ejpam-2346	13	8	also	also	ADV
ejpam-2346	13	9	introduced	introduce	VERB
ejpam-2346	13	10	the	the	DET
ejpam-2346	13	11	concepts	concept	NOUN
ejpam-2346	13	12	of	of	ADP
ejpam-2346	13	13	global	global	ADJ
ejpam-2346	13	14	smoothing	smoothing	NOUN
ejpam-2346	13	15	control	control	NOUN
ejpam-2346	13	16	and	and	CCONJ
ejpam-2346	13	17	gave	give	VERB
ejpam-2346	13	18	an	an	DET
ejpam-2346	13	19	algorithmic	algorithmic	ADJ
ejpam-2346	13	20	description	description	NOUN
ejpam-2346	13	21	of	of	ADP
ejpam-2346	13	22	this	this	DET
ejpam-2346	13	23	method	method	NOUN
ejpam-2346	13	24	.	.	PUNCT
ejpam-2346	14	1	the	the	DET
ejpam-2346	14	2	potential	potential	NOUN
ejpam-2346	14	3	of	of	ADP
ejpam-2346	14	4	the	the	DET
ejpam-2346	14	5	getme	getme	NOUN
ejpam-2346	14	6	based	base	VERB
ejpam-2346	14	7	smoothing	smoothing	NOUN
ejpam-2346	14	8	is	be	AUX
ejpam-2346	14	9	also	also	ADV
ejpam-2346	14	10	illustrated	illustrate	VERB
ejpam-2346	14	11	there	there	ADV
ejpam-2346	14	12	.	.	PUNCT
ejpam-2346	15	1	in	in	ADP
ejpam-2346	15	2	[	[	X
ejpam-2346	15	3	13	13	NUM
ejpam-2346	15	4	]	]	PUNCT
ejpam-2346	15	5	,	,	PUNCT
ejpam-2346	15	6	the	the	DET
ejpam-2346	15	7	generalized	generalized	ADJ
ejpam-2346	15	8	transformation	transformation	NOUN
ejpam-2346	15	9	was	be	AUX
ejpam-2346	15	10	presented	present	VERB
ejpam-2346	15	11	and	and	CCONJ
ejpam-2346	15	12	also	also	ADV
ejpam-2346	15	13	described	describe	VERB
ejpam-2346	15	14	the	the	DET
ejpam-2346	15	15	enhanced	enhance	VERB
ejpam-2346	15	16	getme	getme	NOUN
ejpam-2346	15	17	-	-	PUNCT
ejpam-2346	15	18	based	base	VERB
ejpam-2346	15	19	smoothing	smoothing	NOUN
ejpam-2346	15	20	by	by	ADP
ejpam-2346	15	21	introducing	introduce	VERB
ejpam-2346	15	22	the	the	DET
ejpam-2346	15	23	concepts	concept	NOUN
ejpam-2346	15	24	and	and	CCONJ
ejpam-2346	15	25	quality	quality	NOUN
ejpam-2346	15	26	metric	metric	NOUN
ejpam-2346	15	27	used	use	VERB
ejpam-2346	15	28	for	for	ADP
ejpam-2346	15	29	smoothing	smoothing	NOUN
ejpam-2346	15	30	and	and	CCONJ
ejpam-2346	15	31	termination	termination	NOUN
ejpam-2346	15	32	control	control	NOUN
ejpam-2346	15	33	.	.	PUNCT
ejpam-2346	16	1	numerical	numerical	ADJ
ejpam-2346	16	2	results	result	NOUN
ejpam-2346	16	3	and	and	CCONJ
ejpam-2346	16	4	a	a	DET
ejpam-2346	16	5	comparison	comparison	NOUN
ejpam-2346	16	6	to	to	ADP
ejpam-2346	16	7	other	other	ADJ
ejpam-2346	16	8	smoothing	smooth	VERB
ejpam-2346	16	9	methods	method	NOUN
ejpam-2346	16	10	,	,	PUNCT
ejpam-2346	16	11	both	both	CCONJ
ejpam-2346	16	12	geometrical	geometrical	ADJ
ejpam-2346	16	13	and	and	CCONJ
ejpam-2346	16	14	optimization	optimization	NOUN
ejpam-2346	16	15	-	-	PUNCT
ejpam-2346	16	16	based	base	VERB
ejpam-2346	16	17	were	be	AUX
ejpam-2346	16	18	also	also	ADV
ejpam-2346	16	19	given	give	VERB
ejpam-2346	16	20	.	.	PUNCT
ejpam-2346	17	1	in	in	ADP
ejpam-2346	17	2	[	[	X
ejpam-2346	17	3	12	12	NUM
ejpam-2346	17	4	]	]	PUNCT
ejpam-2346	17	5	,	,	PUNCT
ejpam-2346	17	6	∗corresponding	∗corresponde	VERB
ejpam-2346	17	7	author	author	NOUN
ejpam-2346	17	8	.	.	PUNCT
ejpam-2346	18	1	email	email	NOUN
ejpam-2346	18	2	addresses	address	NOUN
ejpam-2346	18	3	:	:	PUNCT
ejpam-2346	18	4	santu.mathju@gmail.com	santu.mathju@gmail.com	NOUN
ejpam-2346	18	5	(	(	PUNCT
ejpam-2346	18	6	s.	s.	PROPN
ejpam-2346	18	7	dey	dey	PROPN
ejpam-2346	18	8	)	)	PUNCT
ejpam-2346	18	9	,	,	PUNCT
ejpam-2346	18	10	buddha.pal@rediffmail.com	buddha.pal@rediffmail.com	X
ejpam-2346	18	11	(	(	PUNCT
ejpam-2346	18	12	b.	b.	PROPN
ejpam-2346	18	13	pal	pal	PROPN
ejpam-2346	18	14	)	)	PUNCT
ejpam-2346	18	15	,	,	PUNCT
ejpam-2346	18	16	bhattachar1968@yahoo.co.in	bhattachar1968@yahoo.co.in	PROPN
ejpam-2346	18	17	(	(	PUNCT
ejpam-2346	18	18	a.	a.	NOUN
ejpam-2346	18	19	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	18	20	)	)	PUNCT
ejpam-2346	18	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2346	19	1	315	315	NUM
ejpam-2346	19	2	c	c	NOUN
ejpam-2346	19	3	©	©	PROPN
ejpam-2346	19	4	2018	2018	NUM
ejpam-2346	19	5	ejpam	ejpam	VERB
ejpam-2346	19	6	all	all	DET
ejpam-2346	19	7	rights	right	NOUN
ejpam-2346	19	8	reserved	reserve	VERB
ejpam-2346	19	9	.	.	PUNCT
ejpam-2346	20	1	s.	s.	PROPN
ejpam-2346	20	2	dey	dey	PROPN
ejpam-2346	20	3	,	,	PUNCT
ejpam-2346	20	4	b.	b.	PROPN
ejpam-2346	20	5	pal	pal	PROPN
ejpam-2346	20	6	,	,	PUNCT
ejpam-2346	20	7	a.	a.	NOUN
ejpam-2346	20	8	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	20	9	/	/	SYM
ejpam-2346	20	10	eur	eur	PROPN
ejpam-2346	20	11	.	.	PUNCT
ejpam-2346	21	1	j.	j.	PROPN
ejpam-2346	21	2	pure	pure	PROPN
ejpam-2346	21	3	appl	appl	PROPN
ejpam-2346	21	4	.	.	PROPN
ejpam-2346	21	5	math	math	PROPN
ejpam-2346	21	6	,	,	PUNCT
ejpam-2346	21	7	11	11	NUM
ejpam-2346	21	8	(	(	PUNCT
ejpam-2346	21	9	1	1	NUM
ejpam-2346	21	10	)	)	PUNCT
ejpam-2346	21	11	(	(	PUNCT
ejpam-2346	21	12	2018	2018	NUM
ejpam-2346	21	13	)	)	PUNCT
ejpam-2346	21	14	,	,	PUNCT
ejpam-2346	21	15	315	315	NUM
ejpam-2346	21	16	-	-	SYM
ejpam-2346	21	17	330	330	NUM
ejpam-2346	21	18	316	316	NUM
ejpam-2346	21	19	the	the	DET
ejpam-2346	21	20	simultaneous	simultaneous	ADJ
ejpam-2346	21	21	getme	getme	NOUN
ejpam-2346	21	22	smoothing	smooth	VERB
ejpam-2346	21	23	algorithm	algorithm	NOUN
ejpam-2346	21	24	based	base	VERB
ejpam-2346	21	25	on	on	ADP
ejpam-2346	21	26	transforming	transform	VERB
ejpam-2346	21	27	all	all	DET
ejpam-2346	21	28	mesh	mesh	NOUN
ejpam-2346	21	29	elements	element	NOUN
ejpam-2346	21	30	and	and	CCONJ
ejpam-2346	21	31	the	the	DET
ejpam-2346	21	32	sequential	sequential	ADJ
ejpam-2346	21	33	getme	getme	NOUN
ejpam-2346	21	34	algorithm	algorithm	NOUN
ejpam-2346	21	35	based	base	VERB
ejpam-2346	21	36	on	on	ADP
ejpam-2346	21	37	transforming	transform	VERB
ejpam-2346	21	38	only	only	ADV
ejpam-2346	21	39	the	the	DET
ejpam-2346	21	40	worst	bad	ADJ
ejpam-2346	21	41	mesh	mesh	NOUN
ejpam-2346	21	42	element	element	NOUN
ejpam-2346	21	43	were	be	AUX
ejpam-2346	21	44	described	describe	VERB
ejpam-2346	21	45	.	.	PUNCT
ejpam-2346	22	1	basically	basically	ADV
ejpam-2346	22	2	,	,	PUNCT
ejpam-2346	22	3	the	the	DET
ejpam-2346	22	4	geometric	geometric	ADJ
ejpam-2346	22	5	element	element	NOUN
ejpam-2346	22	6	transformation	transformation	NOUN
ejpam-2346	22	7	method	method	NOUN
ejpam-2346	22	8	(	(	PUNCT
ejpam-2346	22	9	getme	getme	NOUN
ejpam-2346	22	10	)	)	PUNCT
ejpam-2346	22	11	is	be	AUX
ejpam-2346	22	12	a	a	DET
ejpam-2346	22	13	geometry	geometry	NOUN
ejpam-2346	22	14	-	-	PUNCT
ejpam-2346	22	15	based	base	VERB
ejpam-2346	22	16	smoothing	smoothing	NOUN
ejpam-2346	22	17	method	method	NOUN
ejpam-2346	22	18	for	for	ADP
ejpam-2346	22	19	mixed	mixed	ADJ
ejpam-2346	22	20	and	and	CCONJ
ejpam-2346	22	21	non	non	ADJ
ejpam-2346	22	22	-	-	ADJ
ejpam-2346	22	23	mixed	mixed	ADJ
ejpam-2346	22	24	meshes	mesh	NOUN
ejpam-2346	22	25	.	.	PUNCT
ejpam-2346	23	1	it	it	PRON
ejpam-2346	23	2	is	be	AUX
ejpam-2346	23	3	based	base	VERB
ejpam-2346	23	4	on	on	ADP
ejpam-2346	23	5	a	a	DET
ejpam-2346	23	6	simple	simple	ADJ
ejpam-2346	23	7	geometric	geometric	ADJ
ejpam-2346	23	8	transformation	transformation	NOUN
ejpam-2346	23	9	applicable	applicable	ADJ
ejpam-2346	23	10	to	to	ADP
ejpam-2346	23	11	elements	element	NOUN
ejpam-2346	23	12	bounded	bound	VERB
ejpam-2346	23	13	by	by	ADP
ejpam-2346	23	14	polygons	polygon	NOUN
ejpam-2346	23	15	with	with	ADP
ejpam-2346	23	16	an	an	DET
ejpam-2346	23	17	arbitrary	arbitrary	ADJ
ejpam-2346	23	18	number	number	NOUN
ejpam-2346	23	19	of	of	ADP
ejpam-2346	23	20	nodes	node	NOUN
ejpam-2346	23	21	.	.	PUNCT
ejpam-2346	24	1	the	the	DET
ejpam-2346	24	2	transformation	transformation	NOUN
ejpam-2346	24	3	,	,	PUNCT
ejpam-2346	24	4	if	if	SCONJ
ejpam-2346	24	5	applied	apply	VERB
ejpam-2346	24	6	iteratively	iteratively	ADV
ejpam-2346	24	7	,	,	PUNCT
ejpam-2346	24	8	leads	lead	VERB
ejpam-2346	24	9	to	to	ADP
ejpam-2346	24	10	a	a	DET
ejpam-2346	24	11	regularization	regularization	NOUN
ejpam-2346	24	12	of	of	ADP
ejpam-2346	24	13	the	the	DET
ejpam-2346	24	14	polygons	polygon	NOUN
ejpam-2346	24	15	.	.	PUNCT
ejpam-2346	25	1	global	global	ADJ
ejpam-2346	25	2	mesh	mesh	NOUN
ejpam-2346	25	3	smoothing	smoothing	NOUN
ejpam-2346	25	4	is	be	AUX
ejpam-2346	25	5	accomplished	accomplish	VERB
ejpam-2346	25	6	by	by	ADP
ejpam-2346	25	7	averaging	average	VERB
ejpam-2346	25	8	the	the	DET
ejpam-2346	25	9	new	new	ADJ
ejpam-2346	25	10	node	node	NOUN
ejpam-2346	25	11	positions	position	NOUN
ejpam-2346	25	12	obtained	obtain	VERB
ejpam-2346	25	13	by	by	ADP
ejpam-2346	25	14	local	local	ADJ
ejpam-2346	25	15	element	element	NOUN
ejpam-2346	25	16	transformations	transformation	NOUN
ejpam-2346	25	17	.	.	PUNCT
ejpam-2346	26	1	thereby	thereby	ADV
ejpam-2346	26	2	,	,	PUNCT
ejpam-2346	26	3	the	the	DET
ejpam-2346	26	4	choice	choice	NOUN
ejpam-2346	26	5	of	of	ADP
ejpam-2346	26	6	transformation	transformation	NOUN
ejpam-2346	26	7	parameters	parameter	NOUN
ejpam-2346	26	8	as	as	ADV
ejpam-2346	26	9	well	well	ADV
ejpam-2346	26	10	as	as	ADP
ejpam-2346	26	11	averaging	average	VERB
ejpam-2346	26	12	weights	weight	NOUN
ejpam-2346	26	13	can	can	AUX
ejpam-2346	26	14	be	be	AUX
ejpam-2346	26	15	based	base	VERB
ejpam-2346	26	16	on	on	ADP
ejpam-2346	26	17	the	the	DET
ejpam-2346	26	18	element	element	NOUN
ejpam-2346	26	19	quality	quality	NOUN
ejpam-2346	26	20	which	which	PRON
ejpam-2346	26	21	leads	lead	VERB
ejpam-2346	26	22	to	to	ADP
ejpam-2346	26	23	high	high	ADJ
ejpam-2346	26	24	quality	quality	NOUN
ejpam-2346	26	25	results	result	NOUN
ejpam-2346	26	26	.	.	PUNCT
ejpam-2346	27	1	the	the	DET
ejpam-2346	27	2	most	most	ADV
ejpam-2346	27	3	usual	usual	ADJ
ejpam-2346	27	4	technique	technique	NOUN
ejpam-2346	27	5	to	to	PART
ejpam-2346	27	6	improve	improve	VERB
ejpam-2346	27	7	the	the	DET
ejpam-2346	27	8	quality	quality	NOUN
ejpam-2346	27	9	of	of	ADP
ejpam-2346	27	10	a	a	DET
ejpam-2346	27	11	valid	valid	ADJ
ejpam-2346	27	12	mesh	mesh	NOUN
ejpam-2346	27	13	,	,	PUNCT
ejpam-2346	27	14	that	that	ADV
ejpam-2346	27	15	is	is	ADV
ejpam-2346	27	16	,	,	PUNCT
ejpam-2346	27	17	one	one	NUM
ejpam-2346	27	18	that	that	PRON
ejpam-2346	27	19	does	do	AUX
ejpam-2346	27	20	not	not	PART
ejpam-2346	27	21	have	have	VERB
ejpam-2346	27	22	inverted	invert	VERB
ejpam-2346	27	23	elements	element	NOUN
ejpam-2346	27	24	,	,	PUNCT
ejpam-2346	27	25	are	be	AUX
ejpam-2346	27	26	based	base	VERB
ejpam-2346	27	27	upon	upon	SCONJ
ejpam-2346	27	28	local	local	ADJ
ejpam-2346	27	29	smoothing	smoothing	NOUN
ejpam-2346	27	30	.	.	PUNCT
ejpam-2346	28	1	usually	usually	ADV
ejpam-2346	28	2	,	,	PUNCT
ejpam-2346	28	3	objective	objective	ADJ
ejpam-2346	28	4	functions	function	NOUN
ejpam-2346	28	5	are	be	AUX
ejpam-2346	28	6	appropriate	appropriate	ADJ
ejpam-2346	28	7	to	to	PART
ejpam-2346	28	8	improve	improve	VERB
ejpam-2346	28	9	the	the	DET
ejpam-2346	28	10	quality	quality	NOUN
ejpam-2346	28	11	of	of	ADP
ejpam-2346	28	12	a	a	DET
ejpam-2346	28	13	valid	valid	ADJ
ejpam-2346	28	14	mesh	mesh	NOUN
ejpam-2346	28	15	,	,	PUNCT
ejpam-2346	28	16	but	but	CCONJ
ejpam-2346	28	17	they	they	PRON
ejpam-2346	28	18	do	do	AUX
ejpam-2346	28	19	not	not	PART
ejpam-2346	28	20	work	work	VERB
ejpam-2346	28	21	properly	properly	ADV
ejpam-2346	28	22	when	when	SCONJ
ejpam-2346	28	23	there	there	PRON
ejpam-2346	28	24	are	be	VERB
ejpam-2346	28	25	inverted	inverted	ADJ
ejpam-2346	28	26	elements	element	NOUN
ejpam-2346	28	27	.	.	PUNCT
ejpam-2346	29	1	to	to	PART
ejpam-2346	29	2	avoid	avoid	VERB
ejpam-2346	29	3	this	this	DET
ejpam-2346	29	4	problem	problem	NOUN
ejpam-2346	29	5	we	we	PRON
ejpam-2346	29	6	can	can	AUX
ejpam-2346	29	7	proceed	proceed	VERB
ejpam-2346	29	8	as	as	ADP
ejpam-2346	29	9	freitag	freitag	PROPN
ejpam-2346	29	10	et	et	PROPN
ejpam-2346	29	11	al	al	PROPN
ejpam-2346	29	12	in	in	ADP
ejpam-2346	29	13	[	[	X
ejpam-2346	29	14	3–5	3–5	NOUN
ejpam-2346	29	15	]	]	PUNCT
ejpam-2346	29	16	.	.	PUNCT
ejpam-2346	30	1	in	in	ADP
ejpam-2346	30	2	this	this	DET
ejpam-2346	30	3	paper	paper	NOUN
ejpam-2346	30	4	,	,	PUNCT
ejpam-2346	30	5	we	we	PRON
ejpam-2346	30	6	have	have	AUX
ejpam-2346	30	7	defined	define	VERB
ejpam-2346	30	8	the	the	DET
ejpam-2346	30	9	characterization	characterization	NOUN
ejpam-2346	30	10	of	of	ADP
ejpam-2346	30	11	energy	energy	NOUN
ejpam-2346	30	12	function	function	NOUN
ejpam-2346	30	13	of	of	ADP
ejpam-2346	30	14	a	a	DET
ejpam-2346	30	15	heptahedra	heptahedra	NOUN
ejpam-2346	30	16	using	use	VERB
ejpam-2346	30	17	base	base	NOUN
ejpam-2346	30	18	diagonal	diagonal	ADJ
ejpam-2346	30	19	apex	apex	NOUN
ejpam-2346	30	20	method	method	NOUN
ejpam-2346	30	21	(	(	PUNCT
ejpam-2346	30	22	bdame	bdame	PROPN
ejpam-2346	30	23	)	)	PUNCT
ejpam-2346	30	24	.	.	PUNCT
ejpam-2346	31	1	also	also	ADV
ejpam-2346	31	2	,	,	PUNCT
ejpam-2346	31	3	we	we	PRON
ejpam-2346	31	4	have	have	AUX
ejpam-2346	31	5	defined	define	VERB
ejpam-2346	31	6	the	the	DET
ejpam-2346	31	7	new	new	ADJ
ejpam-2346	31	8	apex	apex	NOUN
ejpam-2346	31	9	transformation	transformation	NOUN
ejpam-2346	31	10	of	of	ADP
ejpam-2346	31	11	heptahedron	heptahedron	NOUN
ejpam-2346	31	12	whose	whose	DET
ejpam-2346	31	13	base	base	NOUN
ejpam-2346	31	14	points	point	NOUN
ejpam-2346	31	15	are	be	AUX
ejpam-2346	31	16	fixed	fix	VERB
ejpam-2346	31	17	.	.	PUNCT
ejpam-2346	32	1	then	then	ADV
ejpam-2346	32	2	we	we	PRON
ejpam-2346	32	3	have	have	AUX
ejpam-2346	32	4	discussed	discuss	VERB
ejpam-2346	32	5	regularization	regularization	NOUN
ejpam-2346	32	6	properties	property	NOUN
ejpam-2346	32	7	of	of	ADP
ejpam-2346	32	8	a	a	DET
ejpam-2346	32	9	heptahedra	heptahedra	NOUN
ejpam-2346	32	10	and	and	CCONJ
ejpam-2346	32	11	tried	try	VERB
ejpam-2346	32	12	to	to	PART
ejpam-2346	32	13	regularize	regularize	VERB
ejpam-2346	32	14	by	by	ADP
ejpam-2346	32	15	using	use	VERB
ejpam-2346	32	16	geometric	geometric	ADJ
ejpam-2346	32	17	element	element	NOUN
ejpam-2346	32	18	transformation	transformation	NOUN
ejpam-2346	32	19	method	method	NOUN
ejpam-2346	32	20	(	(	PUNCT
ejpam-2346	32	21	getme	getme	NOUN
ejpam-2346	32	22	)	)	PUNCT
ejpam-2346	32	23	.	.	PUNCT
ejpam-2346	33	1	finally	finally	ADV
ejpam-2346	33	2	we	we	PRON
ejpam-2346	33	3	have	have	AUX
ejpam-2346	33	4	studied	study	VERB
ejpam-2346	33	5	the	the	DET
ejpam-2346	33	6	characterization	characterization	NOUN
ejpam-2346	33	7	of	of	ADP
ejpam-2346	33	8	energy	energy	NOUN
ejpam-2346	33	9	function	function	NOUN
ejpam-2346	33	10	of	of	ADP
ejpam-2346	33	11	a	a	DET
ejpam-2346	33	12	particular	particular	ADJ
ejpam-2346	33	13	type	type	NOUN
ejpam-2346	33	14	of	of	ADP
ejpam-2346	33	15	heptahedron	heptahedron	NOUN
ejpam-2346	33	16	using	use	VERB
ejpam-2346	33	17	getme	getme	NOUN
ejpam-2346	33	18	and	and	CCONJ
ejpam-2346	33	19	bdame	bdame	NOUN
ejpam-2346	33	20	.	.	PUNCT
ejpam-2346	34	1	2	2	X
ejpam-2346	34	2	.	.	X
ejpam-2346	34	3	characterization	characterization	NOUN
ejpam-2346	34	4	of	of	ADP
ejpam-2346	34	5	energy	energy	NOUN
ejpam-2346	34	6	function	function	NOUN
ejpam-2346	34	7	of	of	ADP
ejpam-2346	34	8	a	a	DET
ejpam-2346	34	9	heptahedron	heptahedron	NOUN
ejpam-2346	34	10	for	for	ADP
ejpam-2346	34	11	a	a	DET
ejpam-2346	34	12	3	3	NUM
ejpam-2346	34	13	-	-	PUNCT
ejpam-2346	34	14	complex	complex	NOUN
ejpam-2346	34	15	,	,	PUNCT
ejpam-2346	34	16	the	the	DET
ejpam-2346	34	17	cost	cost	NOUN
ejpam-2346	34	18	function	function	NOUN
ejpam-2346	34	19	referred	refer	VERB
ejpam-2346	34	20	as	as	ADP
ejpam-2346	34	21	the	the	DET
ejpam-2346	34	22	energy	energy	NOUN
ejpam-2346	34	23	function	function	NOUN
ejpam-2346	34	24	that	that	PRON
ejpam-2346	34	25	discussed	discuss	VERB
ejpam-2346	34	26	in	in	ADP
ejpam-2346	34	27	[	[	X
ejpam-2346	34	28	10	10	NUM
ejpam-2346	34	29	]	]	PUNCT
ejpam-2346	34	30	.	.	PUNCT
ejpam-2346	35	1	but	but	CCONJ
ejpam-2346	35	2	,	,	PUNCT
ejpam-2346	35	3	we	we	PRON
ejpam-2346	35	4	can	can	AUX
ejpam-2346	35	5	not	not	PART
ejpam-2346	35	6	estimate	estimate	VERB
ejpam-2346	35	7	the	the	DET
ejpam-2346	35	8	energy	energy	NOUN
ejpam-2346	35	9	function	function	NOUN
ejpam-2346	35	10	of	of	ADP
ejpam-2346	35	11	all	all	DET
ejpam-2346	35	12	3	3	NUM
ejpam-2346	35	13	-	-	PUNCT
ejpam-2346	35	14	d	d	NOUN
ejpam-2346	35	15	shapes	shape	NOUN
ejpam-2346	35	16	.	.	PUNCT
ejpam-2346	36	1	in	in	ADP
ejpam-2346	36	2	[	[	X
ejpam-2346	36	3	8	8	NUM
ejpam-2346	36	4	]	]	PUNCT
ejpam-2346	36	5	,	,	PUNCT
ejpam-2346	36	6	the	the	DET
ejpam-2346	36	7	chacterization	chacterization	NOUN
ejpam-2346	36	8	of	of	ADP
ejpam-2346	36	9	energy	energy	NOUN
ejpam-2346	36	10	function	function	NOUN
ejpam-2346	36	11	of	of	ADP
ejpam-2346	36	12	pentahedron	pentahedron	NOUN
ejpam-2346	36	13	have	have	AUX
ejpam-2346	36	14	been	be	AUX
ejpam-2346	36	15	defined	define	VERB
ejpam-2346	36	16	.	.	PUNCT
ejpam-2346	37	1	in	in	ADP
ejpam-2346	37	2	this	this	DET
ejpam-2346	37	3	paper	paper	NOUN
ejpam-2346	37	4	,	,	PUNCT
ejpam-2346	37	5	we	we	PRON
ejpam-2346	37	6	shall	shall	AUX
ejpam-2346	37	7	try	try	VERB
ejpam-2346	37	8	to	to	PART
ejpam-2346	37	9	estimate	estimate	VERB
ejpam-2346	37	10	the	the	DET
ejpam-2346	37	11	energy	energy	NOUN
ejpam-2346	37	12	function	function	NOUN
ejpam-2346	37	13	of	of	ADP
ejpam-2346	37	14	heptahedron	heptahedron	NOUN
ejpam-2346	37	15	by	by	ADP
ejpam-2346	37	16	base	base	NOUN
ejpam-2346	37	17	diagonal	diagonal	ADJ
ejpam-2346	37	18	apex	apex	NOUN
ejpam-2346	37	19	method	method	NOUN
ejpam-2346	37	20	(	(	PUNCT
ejpam-2346	37	21	bdame	bdame	PROPN
ejpam-2346	37	22	)	)	PUNCT
ejpam-2346	37	23	.	.	PUNCT
ejpam-2346	38	1	2.1	2.1	NUM
ejpam-2346	38	2	base	base	NOUN
ejpam-2346	38	3	diagonal	diagonal	ADJ
ejpam-2346	38	4	apex	apex	NOUN
ejpam-2346	38	5	method(bdame	method(bdame	PROPN
ejpam-2346	38	6	):	):	PUNCT
ejpam-2346	38	7	in	in	ADP
ejpam-2346	38	8	[	[	X
ejpam-2346	38	9	8	8	NUM
ejpam-2346	38	10	]	]	PUNCT
ejpam-2346	38	11	,	,	PUNCT
ejpam-2346	38	12	a.	a.	PROPN
ejpam-2346	38	13	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	38	14	and	and	CCONJ
ejpam-2346	38	15	b.	b.	PROPN
ejpam-2346	38	16	pal	pal	PROPN
ejpam-2346	38	17	have	have	AUX
ejpam-2346	38	18	defined	define	VERB
ejpam-2346	38	19	base	base	ADJ
ejpam-2346	38	20	diagonal	diagonal	ADJ
ejpam-2346	38	21	apex	apex	NOUN
ejpam-2346	38	22	method	method	NOUN
ejpam-2346	38	23	.	.	PUNCT
ejpam-2346	39	1	in	in	ADP
ejpam-2346	39	2	this	this	DET
ejpam-2346	39	3	method	method	NOUN
ejpam-2346	39	4	,	,	PUNCT
ejpam-2346	39	5	we	we	PRON
ejpam-2346	39	6	add	add	VERB
ejpam-2346	39	7	the	the	DET
ejpam-2346	39	8	two	two	NUM
ejpam-2346	39	9	diagonal	diagonal	NOUN
ejpam-2346	39	10	of	of	ADP
ejpam-2346	39	11	the	the	DET
ejpam-2346	39	12	base	base	NOUN
ejpam-2346	39	13	of	of	ADP
ejpam-2346	39	14	the	the	DET
ejpam-2346	39	15	pyramid	pyramid	NOUN
ejpam-2346	39	16	and	and	CCONJ
ejpam-2346	39	17	then	then	ADV
ejpam-2346	39	18	add	add	VERB
ejpam-2346	39	19	between	between	ADP
ejpam-2346	39	20	the	the	DET
ejpam-2346	39	21	intersection	intersection	NOUN
ejpam-2346	39	22	point	point	NOUN
ejpam-2346	39	23	of	of	ADP
ejpam-2346	39	24	the	the	DET
ejpam-2346	39	25	diagonal	diagonal	ADJ
ejpam-2346	39	26	and	and	CCONJ
ejpam-2346	39	27	the	the	DET
ejpam-2346	39	28	apex	apex	NOUN
ejpam-2346	39	29	of	of	ADP
ejpam-2346	39	30	the	the	DET
ejpam-2346	39	31	pyramid	pyramid	NOUN
ejpam-2346	39	32	.	.	PUNCT
ejpam-2346	40	1	this	this	DET
ejpam-2346	40	2	line	line	NOUN
ejpam-2346	40	3	(	(	PUNCT
ejpam-2346	40	4	from	from	ADP
ejpam-2346	40	5	apex	apex	NOUN
ejpam-2346	40	6	to	to	ADP
ejpam-2346	40	7	the	the	DET
ejpam-2346	40	8	intersection	intersection	NOUN
ejpam-2346	40	9	point	point	NOUN
ejpam-2346	40	10	of	of	ADP
ejpam-2346	40	11	the	the	DET
ejpam-2346	40	12	diagonals	diagonal	NOUN
ejpam-2346	40	13	)	)	PUNCT
ejpam-2346	40	14	may	may	AUX
ejpam-2346	40	15	be	be	AUX
ejpam-2346	40	16	the	the	DET
ejpam-2346	40	17	height	height	NOUN
ejpam-2346	40	18	of	of	ADP
ejpam-2346	40	19	the	the	DET
ejpam-2346	40	20	pyramid	pyramid	NOUN
ejpam-2346	40	21	or	or	CCONJ
ejpam-2346	40	22	may	may	AUX
ejpam-2346	40	23	not	not	PART
ejpam-2346	40	24	be	be	AUX
ejpam-2346	40	25	the	the	DET
ejpam-2346	40	26	height	height	NOUN
ejpam-2346	40	27	of	of	ADP
ejpam-2346	40	28	the	the	DET
ejpam-2346	40	29	pyramid	pyramid	NOUN
ejpam-2346	40	30	,	,	PUNCT
ejpam-2346	40	31	totally	totally	ADV
ejpam-2346	40	32	depend	depend	VERB
ejpam-2346	40	33	upon	upon	SCONJ
ejpam-2346	40	34	the	the	DET
ejpam-2346	40	35	type	type	NOUN
ejpam-2346	40	36	of	of	ADP
ejpam-2346	40	37	pyramid	pyramid	NOUN
ejpam-2346	40	38	we	we	PRON
ejpam-2346	40	39	choose	choose	VERB
ejpam-2346	40	40	.	.	PUNCT
ejpam-2346	41	1	if	if	SCONJ
ejpam-2346	41	2	we	we	PRON
ejpam-2346	41	3	follow	follow	VERB
ejpam-2346	41	4	this	this	DET
ejpam-2346	41	5	method	method	NOUN
ejpam-2346	41	6	,	,	PUNCT
ejpam-2346	41	7	we	we	PRON
ejpam-2346	41	8	get	get	VERB
ejpam-2346	41	9	six	six	NUM
ejpam-2346	41	10	3	3	NUM
ejpam-2346	41	11	-	-	PUNCT
ejpam-2346	41	12	simplex	simplex	NOUN
ejpam-2346	41	13	,	,	PUNCT
ejpam-2346	41	14	that	that	ADV
ejpam-2346	41	15	is	is	ADV
ejpam-2346	41	16	,	,	PUNCT
ejpam-2346	41	17	six	six	NUM
ejpam-2346	41	18	tetrahedra	tetrahedron	NOUN
ejpam-2346	41	19	.	.	PUNCT
ejpam-2346	42	1	now	now	ADV
ejpam-2346	42	2	,	,	PUNCT
ejpam-2346	42	3	each	each	DET
ejpam-2346	42	4	tetrahedron	tetrahedron	NOUN
ejpam-2346	42	5	has	have	VERB
ejpam-2346	42	6	a	a	DET
ejpam-2346	42	7	cost	cost	NOUN
ejpam-2346	42	8	function	function	NOUN
ejpam-2346	42	9	or	or	CCONJ
ejpam-2346	42	10	energy	energy	NOUN
ejpam-2346	42	11	function	function	NOUN
ejpam-2346	42	12	.	.	PUNCT
ejpam-2346	43	1	therefore	therefore	ADV
ejpam-2346	43	2	,	,	PUNCT
ejpam-2346	43	3	we	we	PRON
ejpam-2346	43	4	get	get	VERB
ejpam-2346	43	5	six	six	NUM
ejpam-2346	43	6	cost	cost	NOUN
ejpam-2346	43	7	functions	function	NOUN
ejpam-2346	43	8	and	and	CCONJ
ejpam-2346	43	9	then	then	ADV
ejpam-2346	43	10	we	we	PRON
ejpam-2346	43	11	can	can	AUX
ejpam-2346	43	12	easily	easily	ADV
ejpam-2346	43	13	define	define	VERB
ejpam-2346	43	14	cost	cost	NOUN
ejpam-2346	43	15	function	function	NOUN
ejpam-2346	43	16	for	for	ADP
ejpam-2346	43	17	heptahedra	heptahedra	NOUN
ejpam-2346	43	18	and	and	CCONJ
ejpam-2346	43	19	to	to	PART
ejpam-2346	43	20	define	define	VERB
ejpam-2346	43	21	the	the	DET
ejpam-2346	43	22	cost	cost	NOUN
ejpam-2346	43	23	function	function	NOUN
ejpam-2346	43	24	of	of	ADP
ejpam-2346	43	25	3	3	NUM
ejpam-2346	43	26	-	-	PUNCT
ejpam-2346	43	27	d	d	NOUN
ejpam-2346	43	28	shapes	shape	NOUN
ejpam-2346	43	29	except	except	SCONJ
ejpam-2346	43	30	3	3	NUM
ejpam-2346	43	31	-	-	PUNCT
ejpam-2346	43	32	simplex	simplex	NOUN
ejpam-2346	43	33	,	,	PUNCT
ejpam-2346	43	34	we	we	PRON
ejpam-2346	43	35	introduce	introduce	VERB
ejpam-2346	43	36	the	the	DET
ejpam-2346	43	37	function	function	NOUN
ejpam-2346	43	38	h(vi	h(vi	PROPN
ejpam-2346	43	39	,	,	PUNCT
ejpam-2346	43	40	σ	σ	PROPN
ejpam-2346	43	41	n	n	CCONJ
ejpam-2346	43	42	)	)	PUNCT
ejpam-2346	43	43	,	,	PUNCT
ejpam-2346	43	44	the	the	DET
ejpam-2346	43	45	signed	sign	VERB
ejpam-2346	43	46	distance	distance	NOUN
ejpam-2346	43	47	from	from	ADP
ejpam-2346	43	48	c(σn	c(σn	NOUN
ejpam-2346	43	49	)	)	PUNCT
ejpam-2346	43	50	to	to	ADP
ejpam-2346	43	51	aff(σn−1	aff(σn−1	PROPN
ejpam-2346	43	52	i	i	PROPN
ejpam-2346	43	53	)	)	PUNCT
ejpam-2346	43	54	with	with	ADP
ejpam-2346	43	55	convention	convention	NOUN
ejpam-2346	43	56	that	that	PRON
ejpam-2346	43	57	h(vi	h(vi	PROPN
ejpam-2346	43	58	,	,	PUNCT
ejpam-2346	43	59	σ	σ	PROPN
ejpam-2346	43	60	n	n	CCONJ
ejpam-2346	43	61	)	)	PUNCT
ejpam-2346	43	62	≥	≥	NOUN
ejpam-2346	43	63	0	0	NUM
ejpam-2346	43	64	when	when	SCONJ
ejpam-2346	43	65	c(σn	c(σn	ADV
ejpam-2346	43	66	)	)	PUNCT
ejpam-2346	43	67	and	and	CCONJ
ejpam-2346	43	68	vi	vi	PROPN
ejpam-2346	43	69	are	be	AUX
ejpam-2346	43	70	the	the	DET
ejpam-2346	43	71	same	same	ADJ
ejpam-2346	43	72	side	side	NOUN
ejpam-2346	43	73	of	of	ADP
ejpam-2346	43	74	aff(σn−1	aff(σn−1	PROPN
ejpam-2346	43	75	i	i	NOUN
ejpam-2346	43	76	)	)	PUNCT
ejpam-2346	43	77	.	.	PUNCT
ejpam-2346	44	1	here	here	ADV
ejpam-2346	44	2	σn	σn	PRON
ejpam-2346	44	3	are	be	AUX
ejpam-2346	44	4	the	the	DET
ejpam-2346	44	5	n	n	NOUN
ejpam-2346	44	6	-	-	PUNCT
ejpam-2346	44	7	simplex	simplex	NOUN
ejpam-2346	44	8	,	,	PUNCT
ejpam-2346	44	9	c(σn	c(σn	NOUN
ejpam-2346	44	10	)	)	PUNCT
ejpam-2346	44	11	the	the	DET
ejpam-2346	44	12	circumcenter	circumcenter	NOUN
ejpam-2346	44	13	of	of	ADP
ejpam-2346	44	14	the	the	DET
ejpam-2346	44	15	n	n	CCONJ
ejpam-2346	44	16	-	-	PUNCT
ejpam-2346	44	17	simplex	simplex	NOUN
ejpam-2346	44	18	,	,	PUNCT
ejpam-2346	44	19	facet	facet	ADJ
ejpam-2346	44	20	aff(σn−1	aff(σn−1	PROPN
ejpam-2346	44	21	i	i	PROPN
ejpam-2346	44	22	)	)	PUNCT
ejpam-2346	44	23	and	and	CCONJ
ejpam-2346	44	24	vertex	vertex	PROPN
ejpam-2346	44	25	vi	vi	PROPN
ejpam-2346	44	26	.	.	PUNCT
ejpam-2346	45	1	we	we	PRON
ejpam-2346	45	2	have	have	AUX
ejpam-2346	45	3	worked	work	VERB
ejpam-2346	45	4	on	on	ADP
ejpam-2346	45	5	all	all	DET
ejpam-2346	45	6	3	3	NUM
ejpam-2346	45	7	-	-	SYM
ejpam-2346	45	8	d	d	NUM
ejpam-2346	45	9	figures	figure	NOUN
ejpam-2346	45	10	,	,	PUNCT
ejpam-2346	45	11	so	so	SCONJ
ejpam-2346	45	12	in	in	ADP
ejpam-2346	45	13	that	that	DET
ejpam-2346	45	14	case	case	NOUN
ejpam-2346	45	15	n	n	NOUN
ejpam-2346	45	16	=	=	SYM
ejpam-2346	45	17	3	3	X
ejpam-2346	45	18	.	.	PUNCT
ejpam-2346	46	1	the	the	DET
ejpam-2346	46	2	magnitude	magnitude	NOUN
ejpam-2346	46	3	of	of	ADP
ejpam-2346	46	4	h(vi	h(vi	PROPN
ejpam-2346	46	5	,	,	PUNCT
ejpam-2346	46	6	σ	σ	PROPN
ejpam-2346	46	7	n	n	CCONJ
ejpam-2346	46	8	)	)	PUNCT
ejpam-2346	46	9	s.	s.	PROPN
ejpam-2346	46	10	dey	dey	PROPN
ejpam-2346	46	11	,	,	PUNCT
ejpam-2346	46	12	b.	b.	PROPN
ejpam-2346	46	13	pal	pal	PROPN
ejpam-2346	46	14	,	,	PUNCT
ejpam-2346	46	15	a.	a.	NOUN
ejpam-2346	46	16	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	46	17	/	/	SYM
ejpam-2346	46	18	eur	eur	PROPN
ejpam-2346	46	19	.	.	PUNCT
ejpam-2346	47	1	j.	j.	PROPN
ejpam-2346	47	2	pure	pure	PROPN
ejpam-2346	47	3	appl	appl	PROPN
ejpam-2346	47	4	.	.	PROPN
ejpam-2346	47	5	math	math	PROPN
ejpam-2346	47	6	,	,	PUNCT
ejpam-2346	47	7	11	11	NUM
ejpam-2346	47	8	(	(	PUNCT
ejpam-2346	47	9	1	1	NUM
ejpam-2346	47	10	)	)	PUNCT
ejpam-2346	47	11	(	(	PUNCT
ejpam-2346	47	12	2018	2018	NUM
ejpam-2346	47	13	)	)	PUNCT
ejpam-2346	47	14	,	,	PUNCT
ejpam-2346	47	15	315	315	NUM
ejpam-2346	47	16	-	-	SYM
ejpam-2346	47	17	330	330	NUM
ejpam-2346	47	18	317	317	NUM
ejpam-2346	47	19	can	can	AUX
ejpam-2346	47	20	be	be	AUX
ejpam-2346	47	21	treated	treat	VERB
ejpam-2346	47	22	as	as	ADP
ejpam-2346	47	23	the	the	DET
ejpam-2346	47	24	distance	distance	NOUN
ejpam-2346	47	25	between	between	ADP
ejpam-2346	47	26	c(σn	c(σn	NOUN
ejpam-2346	47	27	)	)	PUNCT
ejpam-2346	47	28	and	and	CCONJ
ejpam-2346	47	29	c(σn−1	c(σn−1	NUM
ejpam-2346	47	30	i	i	NOUN
ejpam-2346	47	31	)	)	PUNCT
ejpam-2346	47	32	,	,	PUNCT
ejpam-2346	47	33	and	and	CCONJ
ejpam-2346	47	34	its	its	PRON
ejpam-2346	47	35	sign	sign	NOUN
ejpam-2346	47	36	can	can	AUX
ejpam-2346	47	37	be	be	AUX
ejpam-2346	47	38	computed	compute	VERB
ejpam-2346	47	39	by	by	ADP
ejpam-2346	47	40	testing	test	VERB
ejpam-2346	47	41	whether	whether	SCONJ
ejpam-2346	47	42	c(σn	c(σn	NOUN
ejpam-2346	47	43	)	)	PUNCT
ejpam-2346	47	44	and	and	CCONJ
ejpam-2346	47	45	vi	vi	PROPN
ejpam-2346	47	46	have	have	VERB
ejpam-2346	47	47	the	the	DET
ejpam-2346	47	48	same	same	ADJ
ejpam-2346	47	49	orientation	orientation	NOUN
ejpam-2346	47	50	with	with	ADP
ejpam-2346	47	51	respect	respect	NOUN
ejpam-2346	47	52	to	to	ADP
ejpam-2346	47	53	aff(σn−1	aff(σn−1	PROPN
ejpam-2346	47	54	i	i	PROPN
ejpam-2346	47	55	)	)	PUNCT
ejpam-2346	47	56	or	or	CCONJ
ejpam-2346	47	57	not	not	PART
ejpam-2346	47	58	.	.	PUNCT
ejpam-2346	48	1	now	now	ADV
ejpam-2346	48	2	by	by	ADP
ejpam-2346	48	3	bdame	bdame	PROPN
ejpam-2346	48	4	,	,	PUNCT
ejpam-2346	48	5	the	the	DET
ejpam-2346	48	6	heptahedron	heptahedron	NOUN
ejpam-2346	48	7	is	be	AUX
ejpam-2346	48	8	the	the	DET
ejpam-2346	48	9	sum	sum	NOUN
ejpam-2346	48	10	of	of	ADP
ejpam-2346	48	11	the	the	DET
ejpam-2346	48	12	maximum	maximum	ADJ
ejpam-2346	48	13	number	number	NOUN
ejpam-2346	48	14	of	of	ADP
ejpam-2346	48	15	six	six	NUM
ejpam-2346	48	16	3	3	NUM
ejpam-2346	48	17	-	-	PUNCT
ejpam-2346	48	18	simplexes	simplexe	NOUN
ejpam-2346	48	19	.	.	PUNCT
ejpam-2346	49	1	here	here	ADV
ejpam-2346	49	2	we	we	PRON
ejpam-2346	49	3	divide	divide	VERB
ejpam-2346	49	4	the	the	DET
ejpam-2346	49	5	quantity	quantity	NOUN
ejpam-2346	49	6	h(vi	h(vi	PROPN
ejpam-2346	49	7	,	,	PUNCT
ejpam-2346	49	8	σ	σ	PROPN
ejpam-2346	49	9	n	n	CCONJ
ejpam-2346	49	10	)	)	PUNCT
ejpam-2346	49	11	by	by	ADP
ejpam-2346	49	12	the	the	DET
ejpam-2346	49	13	circumradius	circumradius	PROPN
ejpam-2346	49	14	r(σn	r(σn	NOUN
ejpam-2346	49	15	)	)	PUNCT
ejpam-2346	49	16	to	to	PART
ejpam-2346	49	17	get	get	VERB
ejpam-2346	49	18	a	a	DET
ejpam-2346	49	19	quantity	quantity	NOUN
ejpam-2346	49	20	called	call	VERB
ejpam-2346	49	21	cost	cost	NOUN
ejpam-2346	49	22	function	function	NOUN
ejpam-2346	49	23	or	or	CCONJ
ejpam-2346	49	24	energy	energy	NOUN
ejpam-2346	49	25	function	function	NOUN
ejpam-2346	49	26	.	.	PUNCT
ejpam-2346	50	1	observe	observe	VERB
ejpam-2346	50	2	that	that	SCONJ
ejpam-2346	50	3	,	,	PUNCT
ejpam-2346	50	4	−1	−1	NOUN
ejpam-2346	50	5	<	<	X
ejpam-2346	50	6	h(vi	h(vi	PROPN
ejpam-2346	50	7	,	,	PUNCT
ejpam-2346	50	8	σ	σ	PROPN
ejpam-2346	50	9	n)/r(σn	n)/r(σn	PROPN
ejpam-2346	50	10	)	)	PUNCT
ejpam-2346	50	11	<	<	X
ejpam-2346	50	12	1	1	NUM
ejpam-2346	50	13	for	for	ADP
ejpam-2346	50	14	finite	finite	ADJ
ejpam-2346	50	15	σn	σn	NOUN
ejpam-2346	50	16	,	,	PUNCT
ejpam-2346	50	17	as	as	SCONJ
ejpam-2346	50	18	r(σn)2	r(σn)2	PROPN
ejpam-2346	50	19	=	=	SYM
ejpam-2346	50	20	h(vi	h(vi	PROPN
ejpam-2346	50	21	,	,	PUNCT
ejpam-2346	50	22	σ	σ	PROPN
ejpam-2346	50	23	n)2	n)2	PROPN
ejpam-2346	50	24	+	+	PROPN
ejpam-2346	50	25	r(σn−1	r(σn−1	PROPN
ejpam-2346	50	26	i	i	PRON
ejpam-2346	50	27	)	)	PUNCT
ejpam-2346	51	1	2	2	X
ejpam-2346	51	2	.	.	PUNCT
ejpam-2346	51	3	then	then	ADV
ejpam-2346	51	4	,	,	PUNCT
ejpam-2346	51	5	we	we	PRON
ejpam-2346	51	6	have	have	VERB
ejpam-2346	51	7	the	the	DET
ejpam-2346	51	8	following	follow	VERB
ejpam-2346	51	9	theorem	theorem	VERB
ejpam-2346	51	10	.	.	PUNCT
ejpam-2346	51	11	theorem	theorem	VERB
ejpam-2346	51	12	2.1	2.1	NUM
ejpam-2346	51	13	the	the	DET
ejpam-2346	51	14	energy	energy	NOUN
ejpam-2346	51	15	function	function	NOUN
ejpam-2346	51	16	(	(	PUNCT
ejpam-2346	51	17	using	use	VERB
ejpam-2346	51	18	bdame	bdame	PROPN
ejpam-2346	51	19	)	)	PUNCT
ejpam-2346	51	20	fp(σ	fp(σ	PUNCT
ejpam-2346	51	21	n	n	CCONJ
ejpam-2346	51	22	)	)	PUNCT
ejpam-2346	51	23	=	=	SYM
ejpam-2346	52	1	1	1	NUM
ejpam-2346	52	2	n	n	PRON
ejpam-2346	52	3	∑n	∑n	PROPN
ejpam-2346	52	4	j=1maxv∈σn	j=1maxv∈σn	PROPN
ejpam-2346	52	5	|h(v	|h(v	PROPN
ejpam-2346	52	6	,	,	PUNCT
ejpam-2346	52	7	σ	σ	PROPN
ejpam-2346	52	8	n	n	PROPN
ejpam-2346	52	9	j	j	PROPN
ejpam-2346	52	10	)	)	PUNCT
ejpam-2346	53	1	r(σn	r(σn	PROPN
ejpam-2346	53	2	j	j	PROPN
ejpam-2346	53	3	)	)	PUNCT
ejpam-2346	54	1	|	|	ADV
ejpam-2346	54	2	,	,	PUNCT
ejpam-2346	54	3	where	where	SCONJ
ejpam-2346	54	4	n	n	PRON
ejpam-2346	54	5	is	be	AUX
ejpam-2346	54	6	number	number	NOUN
ejpam-2346	54	7	of	of	ADP
ejpam-2346	54	8	tetrahedrons	tetrahedron	NOUN
ejpam-2346	54	9	obtained	obtain	VERB
ejpam-2346	54	10	using	use	VERB
ejpam-2346	54	11	bdame	bdame	NOUN
ejpam-2346	54	12	of	of	ADP
ejpam-2346	54	13	a	a	DET
ejpam-2346	54	14	3d	3d	NUM
ejpam-2346	54	15	-	-	PUNCT
ejpam-2346	54	16	figure	figure	NOUN
ejpam-2346	54	17	(	(	PUNCT
ejpam-2346	54	18	pentahedron	pentahedron	NOUN
ejpam-2346	54	19	,	,	PUNCT
ejpam-2346	54	20	hexahedron	hexahedron	NOUN
ejpam-2346	54	21	,	,	PUNCT
ejpam-2346	54	22	decahedron	decahedron	NOUN
ejpam-2346	54	23	,	,	PUNCT
ejpam-2346	54	24	octahedron	octahedron	NOUN
ejpam-2346	54	25	,	,	PUNCT
ejpam-2346	54	26	...	...	PUNCT
ejpam-2346	54	27	,	,	PUNCT
ejpam-2346	54	28	etc	etc	X
ejpam-2346	54	29	)	)	PUNCT
ejpam-2346	54	30	,	,	PUNCT
ejpam-2346	54	31	always	always	ADV
ejpam-2346	54	32	lies	lie	VERB
ejpam-2346	54	33	between	between	ADP
ejpam-2346	54	34	0	0	NUM
ejpam-2346	54	35	and	and	CCONJ
ejpam-2346	54	36	1	1	NUM
ejpam-2346	54	37	that	that	PRON
ejpam-2346	54	38	is	be	AUX
ejpam-2346	54	39	,	,	PUNCT
ejpam-2346	54	40	0	0	PUNCT
ejpam-2346	54	41	<	<	X
ejpam-2346	54	42	fp(σ	fp(σ	X
ejpam-2346	54	43	n	n	X
ejpam-2346	54	44	)	)	PUNCT
ejpam-2346	54	45	<	<	X
ejpam-2346	55	1	1	1	X
ejpam-2346	55	2	.	.	PUNCT
ejpam-2346	55	3	the	the	DET
ejpam-2346	55	4	proof	proof	NOUN
ejpam-2346	55	5	of	of	ADP
ejpam-2346	55	6	this	this	DET
ejpam-2346	55	7	theorem	theorem	NOUN
ejpam-2346	55	8	was	be	AUX
ejpam-2346	55	9	already	already	ADV
ejpam-2346	55	10	done	do	VERB
ejpam-2346	55	11	in	in	ADP
ejpam-2346	55	12	[	[	X
ejpam-2346	55	13	16	16	NUM
ejpam-2346	55	14	]	]	PUNCT
ejpam-2346	55	15	.	.	PUNCT
ejpam-2346	56	1	so	so	ADV
ejpam-2346	56	2	,	,	PUNCT
ejpam-2346	56	3	for	for	ADP
ejpam-2346	56	4	our	our	PRON
ejpam-2346	56	5	case	case	NOUN
ejpam-2346	56	6	,	,	PUNCT
ejpam-2346	56	7	the	the	DET
ejpam-2346	56	8	energy	energy	NOUN
ejpam-2346	56	9	function	function	NOUN
ejpam-2346	56	10	of	of	ADP
ejpam-2346	56	11	heptahedron	heptahedron	PROPN
ejpam-2346	56	12	be	be	AUX
ejpam-2346	56	13	fh(σn	fh(σn	ADV
ejpam-2346	56	14	)	)	PUNCT
ejpam-2346	57	1	=	=	SYM
ejpam-2346	57	2	1	1	NUM
ejpam-2346	57	3	6	6	NUM
ejpam-2346	57	4	∑6	∑6	PROPN
ejpam-2346	57	5	j=1maxv∈σn	j=1maxv∈σn	PROPN
ejpam-2346	57	6	|h(v	|h(v	PROPN
ejpam-2346	57	7	,	,	PUNCT
ejpam-2346	57	8	σ	σ	PROPN
ejpam-2346	57	9	n	n	PROPN
ejpam-2346	57	10	j	j	PROPN
ejpam-2346	57	11	)	)	PUNCT
ejpam-2346	58	1	r(σn	r(σn	PROPN
ejpam-2346	58	2	j	j	PROPN
ejpam-2346	58	3	)	)	PUNCT
ejpam-2346	59	1	|	|	ADV
ejpam-2346	59	2	,	,	PUNCT
ejpam-2346	59	3	where	where	SCONJ
ejpam-2346	59	4	h	h	NOUN
ejpam-2346	59	5	stands	stand	VERB
ejpam-2346	59	6	for	for	ADP
ejpam-2346	59	7	heptahedron	heptahedron	NOUN
ejpam-2346	59	8	.	.	PUNCT
ejpam-2346	60	1	3	3	X
ejpam-2346	60	2	.	.	X
ejpam-2346	60	3	methods	method	NOUN
ejpam-2346	60	4	of	of	ADP
ejpam-2346	60	5	transformation	transformation	NOUN
ejpam-2346	60	6	in	in	ADP
ejpam-2346	60	7	this	this	DET
ejpam-2346	60	8	section	section	NOUN
ejpam-2346	60	9	we	we	PRON
ejpam-2346	60	10	use	use	VERB
ejpam-2346	60	11	several	several	ADJ
ejpam-2346	60	12	methods	method	NOUN
ejpam-2346	60	13	of	of	ADP
ejpam-2346	60	14	transformation	transformation	NOUN
ejpam-2346	60	15	to	to	PART
ejpam-2346	60	16	regularize	regularize	VERB
ejpam-2346	60	17	the	the	DET
ejpam-2346	60	18	3	3	NUM
ejpam-2346	60	19	-	-	PUNCT
ejpam-2346	60	20	d	d	NOUN
ejpam-2346	60	21	figure	figure	NOUN
ejpam-2346	60	22	,	,	PUNCT
ejpam-2346	60	23	like	like	ADP
ejpam-2346	60	24	heptahedra	heptahedra	NOUN
ejpam-2346	60	25	.	.	PUNCT
ejpam-2346	61	1	here	here	ADV
ejpam-2346	61	2	,	,	PUNCT
ejpam-2346	61	3	we	we	PRON
ejpam-2346	61	4	define	define	VERB
ejpam-2346	61	5	a	a	DET
ejpam-2346	61	6	new	new	ADJ
ejpam-2346	61	7	apex	apex	NOUN
ejpam-2346	61	8	transformation	transformation	NOUN
ejpam-2346	61	9	where	where	SCONJ
ejpam-2346	61	10	the	the	DET
ejpam-2346	61	11	base	base	NOUN
ejpam-2346	61	12	points	point	NOUN
ejpam-2346	61	13	of	of	ADP
ejpam-2346	61	14	the	the	DET
ejpam-2346	61	15	heptahedron	heptahedron	NOUN
ejpam-2346	61	16	are	be	AUX
ejpam-2346	61	17	fixed	fix	VERB
ejpam-2346	61	18	.	.	PUNCT
ejpam-2346	62	1	3.1	3.1	NUM
ejpam-2346	62	2	transformation	transformation	NOUN
ejpam-2346	62	3	of	of	ADP
ejpam-2346	62	4	heptahedra	heptahedra	PROPN
ejpam-2346	62	5	using	use	VERB
ejpam-2346	62	6	getme	getme	NOUN
ejpam-2346	62	7	:	:	PUNCT
ejpam-2346	62	8	let	let	VERB
ejpam-2346	62	9	h	h	NOUN
ejpam-2346	62	10	:	:	PUNCT
ejpam-2346	62	11	=	=	SYM
ejpam-2346	62	12	(	(	PUNCT
ejpam-2346	62	13	h1	h1	PROPN
ejpam-2346	62	14	,	,	PUNCT
ejpam-2346	62	15	h2	h2	PROPN
ejpam-2346	62	16	,	,	PUNCT
ejpam-2346	62	17	h3	h3	NOUN
ejpam-2346	62	18	,	,	PUNCT
ejpam-2346	62	19	h4	h4	NOUN
ejpam-2346	62	20	,	,	PUNCT
ejpam-2346	62	21	h5	h5	PROPN
ejpam-2346	62	22	,	,	PUNCT
ejpam-2346	62	23	h6	h6	PROPN
ejpam-2346	62	24	,	,	PUNCT
ejpam-2346	62	25	h7	h7	PROPN
ejpam-2346	62	26	)	)	PUNCT
ejpam-2346	62	27	t	t	PROPN
ejpam-2346	62	28	denote	denote	VERB
ejpam-2346	62	29	a	a	DET
ejpam-2346	62	30	heptahedron	heptahedron	NOUN
ejpam-2346	62	31	with	with	ADP
ejpam-2346	62	32	seven	seven	NUM
ejpam-2346	62	33	pairwise	pairwise	NOUN
ejpam-2346	62	34	disjoint	disjoint	NOUN
ejpam-2346	62	35	nodes	nod	VERB
ejpam-2346	62	36	hi	hi	PROPN
ejpam-2346	62	37	∈	∈	PROPN
ejpam-2346	62	38	r3	r3	PROPN
ejpam-2346	62	39	,	,	PUNCT
ejpam-2346	62	40	i	i	PRON
ejpam-2346	62	41	∈	∈	PROPN
ejpam-2346	62	42	{	{	PUNCT
ejpam-2346	62	43	1	1	NUM
ejpam-2346	62	44	,	,	PUNCT
ejpam-2346	62	45	....	....	PUNCT
ejpam-2346	62	46	,	,	PUNCT
ejpam-2346	62	47	7	7	NUM
ejpam-2346	62	48	}	}	PUNCT
ejpam-2346	62	49	,	,	PUNCT
ejpam-2346	62	50	which	which	PRON
ejpam-2346	62	51	are	be	AUX
ejpam-2346	62	52	positively	positively	ADV
ejpam-2346	62	53	oriented	orient	VERB
ejpam-2346	62	54	.	.	PUNCT
ejpam-2346	63	1	let	let	VERB
ejpam-2346	63	2	n1	n1	NOUN
ejpam-2346	63	3	:	:	PUNCT
ejpam-2346	63	4	=	=	SYM
ejpam-2346	63	5	(	(	PUNCT
ejpam-2346	63	6	h7	h7	PROPN
ejpam-2346	63	7	−	−	PROPN
ejpam-2346	63	8	h2)×	h2)×	PROPN
ejpam-2346	63	9	(	(	PUNCT
ejpam-2346	63	10	h3	h3	NOUN
ejpam-2346	63	11	−	−	PROPN
ejpam-2346	63	12	h2	h2	NOUN
ejpam-2346	63	13	)	)	PUNCT
ejpam-2346	63	14	,	,	PUNCT
ejpam-2346	63	15	n2	n2	NOUN
ejpam-2346	63	16	:	:	PUNCT
ejpam-2346	63	17	=	=	SYM
ejpam-2346	63	18	(	(	PUNCT
ejpam-2346	63	19	h7	h7	PROPN
ejpam-2346	63	20	−	−	PROPN
ejpam-2346	63	21	h3)×	h3)×	PROPN
ejpam-2346	63	22	(	(	PUNCT
ejpam-2346	63	23	h4	h4	PROPN
ejpam-2346	63	24	−	−	PROPN
ejpam-2346	63	25	h3	h3	NOUN
ejpam-2346	63	26	)	)	PUNCT
ejpam-2346	63	27	,	,	PUNCT
ejpam-2346	63	28	n3	n3	NOUN
ejpam-2346	63	29	:	:	PUNCT
ejpam-2346	63	30	=	=	SYM
ejpam-2346	63	31	(	(	PUNCT
ejpam-2346	63	32	h7	h7	PROPN
ejpam-2346	63	33	−	−	PROPN
ejpam-2346	63	34	h4)×	h4)×	PROPN
ejpam-2346	63	35	(	(	PUNCT
ejpam-2346	63	36	h5	h5	PROPN
ejpam-2346	63	37	−	−	PROPN
ejpam-2346	63	38	h4	h4	PROPN
ejpam-2346	63	39	)	)	PUNCT
ejpam-2346	63	40	,	,	PUNCT
ejpam-2346	63	41	n4	n4	PROPN
ejpam-2346	63	42	:	:	PUNCT
ejpam-2346	63	43	=	=	SYM
ejpam-2346	63	44	(	(	PUNCT
ejpam-2346	63	45	h7	h7	PROPN
ejpam-2346	63	46	−	−	PROPN
ejpam-2346	63	47	h5)×	h5)×	PROPN
ejpam-2346	63	48	(	(	PUNCT
ejpam-2346	63	49	h6	h6	PROPN
ejpam-2346	63	50	−	−	PROPN
ejpam-2346	63	51	h5	h5	PROPN
ejpam-2346	63	52	)	)	PUNCT
ejpam-2346	63	53	,	,	PUNCT
ejpam-2346	63	54	n5	n5	PROPN
ejpam-2346	63	55	:	:	PUNCT
ejpam-2346	63	56	=	=	SYM
ejpam-2346	63	57	(	(	PUNCT
ejpam-2346	63	58	h6	h6	PROPN
ejpam-2346	63	59	−	−	PROPN
ejpam-2346	64	1	h7)×	h7)×	PROPN
ejpam-2346	64	2	(	(	PUNCT
ejpam-2346	64	3	h1	h1	PROPN
ejpam-2346	64	4	−	−	PROPN
ejpam-2346	64	5	h7	h7	PROPN
ejpam-2346	64	6	)	)	PUNCT
ejpam-2346	64	7	,	,	PUNCT
ejpam-2346	64	8	n6	n6	NOUN
ejpam-2346	64	9	:	:	PUNCT
ejpam-2346	64	10	=	=	SYM
ejpam-2346	64	11	(	(	PUNCT
ejpam-2346	64	12	h1	h1	PROPN
ejpam-2346	64	13	−	−	PROPN
ejpam-2346	64	14	h7)×	h7)×	PROPN
ejpam-2346	64	15	(	(	PUNCT
ejpam-2346	64	16	h2	h2	PROPN
ejpam-2346	64	17	−	−	PROPN
ejpam-2346	64	18	h7	h7	PROPN
ejpam-2346	64	19	)	)	PUNCT
ejpam-2346	64	20	,	,	PUNCT
ejpam-2346	64	21	n7	n7	PROPN
ejpam-2346	64	22	:	:	PUNCT
ejpam-2346	64	23	=	=	SYM
ejpam-2346	64	24	(	(	PUNCT
ejpam-2346	64	25	h5	h5	PROPN
ejpam-2346	64	26	−	−	PROPN
ejpam-2346	64	27	h6)×	h6)×	NOUN
ejpam-2346	64	28	(	(	PUNCT
ejpam-2346	64	29	h1	h1	VERB
ejpam-2346	64	30	−	−	PROPN
ejpam-2346	64	31	h6	h6	PROPN
ejpam-2346	64	32	)	)	PUNCT
ejpam-2346	64	33	,	,	PUNCT
ejpam-2346	64	34	denote	denote	VERB
ejpam-2346	64	35	the	the	DET
ejpam-2346	64	36	inside	inside	ADV
ejpam-2346	64	37	oriented	orient	VERB
ejpam-2346	64	38	face	face	NOUN
ejpam-2346	64	39	normal	normal	ADJ
ejpam-2346	64	40	of	of	ADP
ejpam-2346	64	41	h.	h.	PROPN
ejpam-2346	64	42	a	a	DET
ejpam-2346	64	43	new	new	ADJ
ejpam-2346	64	44	heptahedron	heptahedron	ADJ
ejpam-2346	64	45	h	h	NOUN
ejpam-2346	64	46	′	′	NOUN
ejpam-2346	64	47	with	with	ADP
ejpam-2346	64	48	nodes	node	NOUN
ejpam-2346	64	49	h′i	h′i	PRON
ejpam-2346	64	50	is	be	AUX
ejpam-2346	64	51	derived	derive	VERB
ejpam-2346	64	52	from	from	ADP
ejpam-2346	64	53	h	h	NOUN
ejpam-2346	64	54	by	by	ADP
ejpam-2346	64	55	constructing	construct	VERB
ejpam-2346	64	56	on	on	ADP
ejpam-2346	64	57	each	each	DET
ejpam-2346	64	58	node	node	NOUN
ejpam-2346	64	59	hi	hi	INTJ
ejpam-2346	65	1	the	the	DET
ejpam-2346	65	2	opposing	opposing	ADJ
ejpam-2346	65	3	face	face	NOUN
ejpam-2346	65	4	normal	normal	ADJ
ejpam-2346	65	5	ni	ni	NOUN
ejpam-2346	65	6	scaled	scale	VERB
ejpam-2346	65	7	by	by	ADP
ejpam-2346	65	8	σ/	σ/	NOUN
ejpam-2346	65	9	√	√	PROPN
ejpam-2346	65	10	|ni|	|ni|	PROPN
ejpam-2346	65	11	,	,	PUNCT
ejpam-2346	65	12	where	where	SCONJ
ejpam-2346	65	13	σ	σ	PROPN
ejpam-2346	65	14	∈	∈	PROPN
ejpam-2346	65	15	r+	r+	NOUN
ejpam-2346	65	16	0	0	NUM
ejpam-2346	65	17	.	.	PUNCT
ejpam-2346	66	1	that	that	PRON
ejpam-2346	66	2	is	be	AUX
ejpam-2346	66	3	s.	s.	PROPN
ejpam-2346	66	4	dey	dey	PROPN
ejpam-2346	66	5	,	,	PUNCT
ejpam-2346	66	6	b.	b.	PROPN
ejpam-2346	66	7	pal	pal	PROPN
ejpam-2346	66	8	,	,	PUNCT
ejpam-2346	66	9	a.	a.	NOUN
ejpam-2346	66	10	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	66	11	/	/	SYM
ejpam-2346	66	12	eur	eur	PROPN
ejpam-2346	66	13	.	.	PUNCT
ejpam-2346	67	1	j.	j.	PROPN
ejpam-2346	67	2	pure	pure	PROPN
ejpam-2346	67	3	appl	appl	PROPN
ejpam-2346	67	4	.	.	PROPN
ejpam-2346	67	5	math	math	PROPN
ejpam-2346	67	6	,	,	PUNCT
ejpam-2346	67	7	11	11	NUM
ejpam-2346	67	8	(	(	PUNCT
ejpam-2346	67	9	1	1	NUM
ejpam-2346	67	10	)	)	PUNCT
ejpam-2346	67	11	(	(	PUNCT
ejpam-2346	67	12	2018	2018	NUM
ejpam-2346	67	13	)	)	PUNCT
ejpam-2346	67	14	,	,	PUNCT
ejpam-2346	67	15	315	315	NUM
ejpam-2346	67	16	-	-	SYM
ejpam-2346	67	17	330	330	NUM
ejpam-2346	67	18	318	318	NUM
ejpam-2346	67	19	h	h	NOUN
ejpam-2346	67	20	′	′	NUM
ejpam-2346	68	1	=	=	PUNCT
ejpam-2346	68	2			PROPN
ejpam-2346	68	3			NOUN
ejpam-2346	68	4			NOUN
ejpam-2346	68	5			NOUN
ejpam-2346	68	6			NOUN
ejpam-2346	68	7			NOUN
ejpam-2346	68	8			NOUN
ejpam-2346	68	9			NOUN
ejpam-2346	68	10			NOUN
ejpam-2346	68	11			NOUN
ejpam-2346	68	12	h′1	h′1	VERB
ejpam-2346	68	13	h′2	h′2	NOUN
ejpam-2346	69	1	h′3	h′3	PROPN
ejpam-2346	69	2	h′4	h′4	PROPN
ejpam-2346	69	3	h′5	h′5	X
ejpam-2346	70	1	h′6	h′6	PROPN
ejpam-2346	70	2	h′7	h′7	NOUN
ejpam-2346	70	3			PROPN
ejpam-2346	70	4			NOUN
ejpam-2346	70	5			VERB
ejpam-2346	70	6			NOUN
ejpam-2346	70	7			NOUN
ejpam-2346	70	8			NOUN
ejpam-2346	70	9			NOUN
ejpam-2346	70	10			NOUN
ejpam-2346	70	11			NOUN
ejpam-2346	70	12			PUNCT
ejpam-2346	71	1	:	:	PUNCT
ejpam-2346	71	2	=	=	SYM
ejpam-2346	71	3			PROPN
ejpam-2346	71	4			NOUN
ejpam-2346	71	5			NOUN
ejpam-2346	71	6			NOUN
ejpam-2346	71	7			NOUN
ejpam-2346	71	8			NOUN
ejpam-2346	71	9			NOUN
ejpam-2346	71	10			NOUN
ejpam-2346	71	11			NOUN
ejpam-2346	71	12			NOUN
ejpam-2346	71	13	h1	h1	VERB
ejpam-2346	71	14	h2	h2	PROPN
ejpam-2346	71	15	h3	h3	NOUN
ejpam-2346	71	16	h4	h4	PROPN
ejpam-2346	71	17	h5	h5	PROPN
ejpam-2346	71	18	h6	h6	PROPN
ejpam-2346	71	19	h7	h7	PROPN
ejpam-2346	71	20			PROPN
ejpam-2346	71	21			NOUN
ejpam-2346	71	22			VERB
ejpam-2346	71	23			NOUN
ejpam-2346	71	24			NOUN
ejpam-2346	71	25			NOUN
ejpam-2346	71	26			NOUN
ejpam-2346	71	27			NOUN
ejpam-2346	71	28			NOUN
ejpam-2346	71	29			PUNCT
ejpam-2346	72	1	+	+	CCONJ
ejpam-2346	72	2	σ	σ	NUM
ejpam-2346	72	3			PROPN
ejpam-2346	72	4			NOUN
ejpam-2346	72	5			NOUN
ejpam-2346	72	6			NOUN
ejpam-2346	72	7			NOUN
ejpam-2346	72	8			NOUN
ejpam-2346	72	9			NOUN
ejpam-2346	72	10			NOUN
ejpam-2346	72	11			NOUN
ejpam-2346	72	12			NOUN
ejpam-2346	72	13			NOUN
ejpam-2346	72	14			NOUN
ejpam-2346	72	15			NOUN
ejpam-2346	72	16			NOUN
ejpam-2346	72	17			NOUN
ejpam-2346	72	18			NOUN
ejpam-2346	72	19	1√	1√	ADJ
ejpam-2346	72	20	|n1|	|n1|	NOUN
ejpam-2346	72	21	n1	n1	PROPN
ejpam-2346	72	22	1√	1√	PROPN
ejpam-2346	72	23	|n2|	|n2|	NOUN
ejpam-2346	72	24	n2	n2	PROPN
ejpam-2346	72	25	1√	1√	PROPN
ejpam-2346	72	26	|n3|	|n3|	ADP
ejpam-2346	72	27	n3	n3	PROPN
ejpam-2346	72	28	1√	1√	PROPN
ejpam-2346	72	29	|n4|	|n4|	PROPN
ejpam-2346	72	30	n4	n4	PROPN
ejpam-2346	72	31	1√	1√	PROPN
ejpam-2346	72	32	|n5|	|n5|	NOUN
ejpam-2346	72	33	n5	n5	PROPN
ejpam-2346	72	34	1√	1√	PROPN
ejpam-2346	72	35	|n6|	|n6|	NOUN
ejpam-2346	72	36	n6	n6	PROPN
ejpam-2346	72	37	1√	1√	PROPN
ejpam-2346	72	38	|n7|	|n7|	VERB
ejpam-2346	72	39	n7	n7	PROPN
ejpam-2346	72	40			PROPN
ejpam-2346	72	41			NOUN
ejpam-2346	72	42			VERB
ejpam-2346	72	43			NOUN
ejpam-2346	72	44			NOUN
ejpam-2346	72	45			NOUN
ejpam-2346	72	46			NOUN
ejpam-2346	72	47			NOUN
ejpam-2346	72	48			NOUN
ejpam-2346	72	49			NOUN
ejpam-2346	72	50			NOUN
ejpam-2346	72	51			NOUN
ejpam-2346	72	52			NOUN
ejpam-2346	72	53			NOUN
ejpam-2346	72	54			NOUN
ejpam-2346	72	55			PUNCT
ejpam-2346	73	1	(	(	PUNCT
ejpam-2346	73	2	1	1	X
ejpam-2346	73	3	)	)	PUNCT
ejpam-2346	73	4	it	it	PRON
ejpam-2346	73	5	is	be	AUX
ejpam-2346	73	6	clear	clear	ADJ
ejpam-2346	73	7	that	that	SCONJ
ejpam-2346	73	8	if	if	SCONJ
ejpam-2346	73	9	σ	σ	PROPN
ejpam-2346	73	10	=	=	NOUN
ejpam-2346	73	11	0	0	PUNCT
ejpam-2346	73	12	then	then	ADV
ejpam-2346	73	13	h	h	NOUN
ejpam-2346	73	14	′	′	NOUN
ejpam-2346	74	1	and	and	CCONJ
ejpam-2346	74	2	h	h	NOUN
ejpam-2346	74	3	are	be	AUX
ejpam-2346	74	4	same	same	ADJ
ejpam-2346	74	5	.	.	PUNCT
ejpam-2346	75	1	3.2	3.2	NUM
ejpam-2346	75	2	apex	apex	NOUN
ejpam-2346	75	3	transformation	transformation	NOUN
ejpam-2346	75	4	of	of	ADP
ejpam-2346	75	5	a	a	DET
ejpam-2346	75	6	heptahedron	heptahedron	NOUN
ejpam-2346	75	7	using	use	VERB
ejpam-2346	75	8	getme	getme	NOUN
ejpam-2346	75	9	:	:	PUNCT
ejpam-2346	75	10	apex	apex	NOUN
ejpam-2346	75	11	transformation	transformation	NOUN
ejpam-2346	75	12	means	mean	VERB
ejpam-2346	75	13	,	,	PUNCT
ejpam-2346	75	14	we	we	PRON
ejpam-2346	75	15	transform	transform	VERB
ejpam-2346	75	16	the	the	DET
ejpam-2346	75	17	apex	apex	NOUN
ejpam-2346	75	18	(	(	PUNCT
ejpam-2346	75	19	top	top	ADJ
ejpam-2346	75	20	vertex	vertex	NOUN
ejpam-2346	75	21	)	)	PUNCT
ejpam-2346	75	22	of	of	ADP
ejpam-2346	75	23	the	the	DET
ejpam-2346	75	24	heptahedron	heptahedron	NOUN
ejpam-2346	75	25	using	use	VERB
ejpam-2346	75	26	geometric	geometric	ADJ
ejpam-2346	75	27	element	element	NOUN
ejpam-2346	75	28	transformation	transformation	NOUN
ejpam-2346	75	29	method	method	NOUN
ejpam-2346	75	30	(	(	PUNCT
ejpam-2346	75	31	getme	getme	NOUN
ejpam-2346	75	32	)	)	PUNCT
ejpam-2346	75	33	as	as	SCONJ
ejpam-2346	75	34	discussed	discuss	VERB
ejpam-2346	75	35	in	in	ADP
ejpam-2346	75	36	the	the	DET
ejpam-2346	75	37	article	article	NOUN
ejpam-2346	75	38	(	(	PUNCT
ejpam-2346	75	39	3.1	3.1	NUM
ejpam-2346	75	40	)	)	PUNCT
ejpam-2346	75	41	.	.	PUNCT
ejpam-2346	76	1	so	so	ADV
ejpam-2346	76	2	,	,	PUNCT
ejpam-2346	76	3	we	we	PRON
ejpam-2346	76	4	transform	transform	VERB
ejpam-2346	76	5	h7	h7	PROPN
ejpam-2346	76	6	(	(	PUNCT
ejpam-2346	76	7	apex	apex	PROPN
ejpam-2346	76	8	)	)	PUNCT
ejpam-2346	76	9	to	to	PART
ejpam-2346	76	10	h′7	h′7	NOUN
ejpam-2346	76	11	using	use	VERB
ejpam-2346	76	12	only	only	ADV
ejpam-2346	76	13	the	the	DET
ejpam-2346	76	14	inside	inside	ADJ
ejpam-2346	76	15	oriented	orient	VERB
ejpam-2346	76	16	face	face	NOUN
ejpam-2346	76	17	normal	normal	ADJ
ejpam-2346	76	18	n7	n7	PROPN
ejpam-2346	76	19	,	,	PUNCT
ejpam-2346	76	20	n7	n7	PROPN
ejpam-2346	76	21	:	:	PUNCT
ejpam-2346	76	22	=	=	SYM
ejpam-2346	76	23	(	(	PUNCT
ejpam-2346	76	24	h5	h5	PROPN
ejpam-2346	76	25	−	−	PROPN
ejpam-2346	76	26	h6	h6	PROPN
ejpam-2346	76	27	)	)	PUNCT
ejpam-2346	76	28	×	×	NOUN
ejpam-2346	76	29	(	(	PUNCT
ejpam-2346	76	30	h1	h1	PROPN
ejpam-2346	76	31	−	−	PROPN
ejpam-2346	76	32	h6	h6	PROPN
ejpam-2346	76	33	)	)	PUNCT
ejpam-2346	76	34	of	of	ADP
ejpam-2346	76	35	h.	h.	PROPN
ejpam-2346	76	36	in	in	ADP
ejpam-2346	76	37	that	that	DET
ejpam-2346	76	38	case	case	NOUN
ejpam-2346	76	39	,	,	PUNCT
ejpam-2346	76	40	a	a	DET
ejpam-2346	76	41	new	new	ADJ
ejpam-2346	76	42	heptahedron	heptahedron	NOUN
ejpam-2346	76	43	h	h	NOUN
ejpam-2346	76	44	′	′	NOUN
ejpam-2346	76	45	with	with	ADP
ejpam-2346	76	46	nodes	node	NOUN
ejpam-2346	76	47	h′i	h′i	PRON
ejpam-2346	76	48	is	be	AUX
ejpam-2346	76	49	derived	derive	VERB
ejpam-2346	76	50	from	from	ADP
ejpam-2346	76	51	h	h	NOUN
ejpam-2346	76	52	by	by	ADP
ejpam-2346	76	53	constructing	construct	VERB
ejpam-2346	76	54	the	the	DET
ejpam-2346	76	55	node	node	PROPN
ejpam-2346	76	56	h7	h7	PROPN
ejpam-2346	76	57	,	,	PUNCT
ejpam-2346	76	58	the	the	DET
ejpam-2346	76	59	opposite	opposite	ADJ
ejpam-2346	76	60	face	face	NOUN
ejpam-2346	76	61	normal	normal	ADJ
ejpam-2346	76	62	n7	n7	PROPN
ejpam-2346	76	63	scaled	scale	VERB
ejpam-2346	76	64	by	by	ADP
ejpam-2346	76	65	σ/	σ/	NOUN
ejpam-2346	76	66	√	√	PROPN
ejpam-2346	76	67	|n7|	|n7|	ADJ
ejpam-2346	76	68	,	,	PUNCT
ejpam-2346	76	69	where	where	SCONJ
ejpam-2346	76	70	σ	σ	PROPN
ejpam-2346	76	71	∈	∈	PROPN
ejpam-2346	76	72	r+	r+	NOUN
ejpam-2346	76	73	0	0	PUNCT
ejpam-2346	76	74	.	.	PUNCT
ejpam-2346	77	1	so	so	ADV
ejpam-2346	77	2	,	,	PUNCT
ejpam-2346	77	3	we	we	PRON
ejpam-2346	77	4	have	have	AUX
ejpam-2346	77	5	given	give	VERB
ejpam-2346	77	6	the	the	DET
ejpam-2346	77	7	apex	apex	NOUN
ejpam-2346	77	8	transformation	transformation	NOUN
ejpam-2346	77	9	of	of	ADP
ejpam-2346	77	10	heptahedron	heptahedron	NOUN
ejpam-2346	77	11	as	as	ADP
ejpam-2346	77	12	below	below	ADP
ejpam-2346	77	13	h	h	NOUN
ejpam-2346	77	14	′	′	NUM
ejpam-2346	78	1	=	=	PUNCT
ejpam-2346	78	2			PROPN
ejpam-2346	78	3			NOUN
ejpam-2346	78	4			NOUN
ejpam-2346	78	5			NOUN
ejpam-2346	78	6			NOUN
ejpam-2346	78	7			NOUN
ejpam-2346	78	8			NOUN
ejpam-2346	78	9			NOUN
ejpam-2346	78	10			NOUN
ejpam-2346	78	11			NOUN
ejpam-2346	78	12	h′1	h′1	VERB
ejpam-2346	78	13	h′2	h′2	NOUN
ejpam-2346	79	1	h′3	h′3	PROPN
ejpam-2346	79	2	h′4	h′4	PROPN
ejpam-2346	79	3	h′5	h′5	X
ejpam-2346	80	1	h′6	h′6	PROPN
ejpam-2346	80	2	h′7	h′7	NOUN
ejpam-2346	80	3			PROPN
ejpam-2346	80	4			NOUN
ejpam-2346	80	5			VERB
ejpam-2346	80	6			NOUN
ejpam-2346	80	7			NOUN
ejpam-2346	80	8			NOUN
ejpam-2346	80	9			NOUN
ejpam-2346	80	10			NOUN
ejpam-2346	80	11			NOUN
ejpam-2346	80	12			PUNCT
ejpam-2346	81	1	:	:	PUNCT
ejpam-2346	81	2	=	=	SYM
ejpam-2346	81	3			PROPN
ejpam-2346	81	4			NOUN
ejpam-2346	81	5			NOUN
ejpam-2346	81	6			NOUN
ejpam-2346	81	7			NOUN
ejpam-2346	81	8			NOUN
ejpam-2346	81	9			NOUN
ejpam-2346	81	10			NOUN
ejpam-2346	81	11			NOUN
ejpam-2346	81	12			NOUN
ejpam-2346	81	13	h1	h1	VERB
ejpam-2346	81	14	h2	h2	PROPN
ejpam-2346	81	15	h3	h3	NOUN
ejpam-2346	81	16	h4	h4	PROPN
ejpam-2346	81	17	h5	h5	PROPN
ejpam-2346	81	18	h6	h6	PROPN
ejpam-2346	81	19	h7	h7	PROPN
ejpam-2346	81	20			PROPN
ejpam-2346	81	21			NOUN
ejpam-2346	81	22			VERB
ejpam-2346	81	23			NOUN
ejpam-2346	81	24			NOUN
ejpam-2346	81	25			NOUN
ejpam-2346	81	26			NOUN
ejpam-2346	81	27			NOUN
ejpam-2346	81	28			NOUN
ejpam-2346	81	29			PUNCT
ejpam-2346	82	1	+	+	CCONJ
ejpam-2346	82	2	σ	σ	NUM
ejpam-2346	82	3			PROPN
ejpam-2346	82	4			NOUN
ejpam-2346	82	5			NOUN
ejpam-2346	82	6			NOUN
ejpam-2346	82	7			NOUN
ejpam-2346	82	8			NOUN
ejpam-2346	82	9			NOUN
ejpam-2346	82	10			NOUN
ejpam-2346	82	11			NOUN
ejpam-2346	82	12			NOUN
ejpam-2346	82	13			NOUN
ejpam-2346	82	14	0	0	NUM
ejpam-2346	82	15	0	0	NUM
ejpam-2346	82	16	0	0	NUM
ejpam-2346	82	17	0	0	NUM
ejpam-2346	82	18	0	0	NUM
ejpam-2346	82	19	0	0	NUM
ejpam-2346	82	20	1√	1√	NUM
ejpam-2346	82	21	|n7|	|n7|	NOUN
ejpam-2346	82	22	n7	n7	PROPN
ejpam-2346	82	23			PROPN
ejpam-2346	82	24			NOUN
ejpam-2346	82	25			VERB
ejpam-2346	82	26			NOUN
ejpam-2346	82	27			NOUN
ejpam-2346	82	28			NOUN
ejpam-2346	82	29			NOUN
ejpam-2346	82	30			NOUN
ejpam-2346	82	31			NOUN
ejpam-2346	82	32			NOUN
ejpam-2346	82	33			PUNCT
ejpam-2346	83	1	(	(	PUNCT
ejpam-2346	83	2	2	2	X
ejpam-2346	83	3	)	)	PUNCT
ejpam-2346	83	4	it	it	PRON
ejpam-2346	83	5	is	be	AUX
ejpam-2346	83	6	clear	clear	ADJ
ejpam-2346	84	1	that	that	SCONJ
ejpam-2346	84	2	if	if	SCONJ
ejpam-2346	84	3	σ	σ	PROPN
ejpam-2346	84	4	=	=	NOUN
ejpam-2346	84	5	0	0	PUNCT
ejpam-2346	84	6	then	then	ADV
ejpam-2346	84	7	h	h	NOUN
ejpam-2346	84	8	′	′	NOUN
ejpam-2346	85	1	and	and	CCONJ
ejpam-2346	85	2	h	h	NOUN
ejpam-2346	85	3	are	be	AUX
ejpam-2346	85	4	same	same	ADJ
ejpam-2346	85	5	.	.	PUNCT
ejpam-2346	86	1	3.3	3.3	NUM
ejpam-2346	86	2	new	new	ADJ
ejpam-2346	86	3	heptahedron	heptahedron	NOUN
ejpam-2346	86	4	derived	derive	VERB
ejpam-2346	86	5	from	from	ADP
ejpam-2346	86	6	centroid	centroid	NOUN
ejpam-2346	86	7	transformation	transformation	NOUN
ejpam-2346	86	8	of	of	ADP
ejpam-2346	86	9	a	a	DET
ejpam-2346	86	10	heptahedron	heptahedron	NOUN
ejpam-2346	86	11	using	use	VERB
ejpam-2346	86	12	getme	getme	NOUN
ejpam-2346	86	13	:	:	PUNCT
ejpam-2346	86	14	let	let	VERB
ejpam-2346	86	15	h	h	PROPN
ejpam-2346	86	16	denotes	denote	VERB
ejpam-2346	86	17	a	a	DET
ejpam-2346	86	18	heptahedron	heptahedron	NOUN
ejpam-2346	86	19	with	with	ADP
ejpam-2346	86	20	nodes	node	NOUN
ejpam-2346	86	21	hk	hk	PROPN
ejpam-2346	86	22	and	and	CCONJ
ejpam-2346	86	23	σ	σ	PROPN
ejpam-2346	86	24	∈	∈	PROPN
ejpam-2346	86	25	r+	r+	VERB
ejpam-2346	86	26	an	an	DET
ejpam-2346	86	27	arbitary	arbitary	ADJ
ejpam-2346	86	28	scaling	scaling	NOUN
ejpam-2346	86	29	factor	factor	NOUN
ejpam-2346	86	30	.	.	PUNCT
ejpam-2346	87	1	the	the	DET
ejpam-2346	87	2	nodes	node	NOUN
ejpam-2346	87	3	h′k	h′k	NOUN
ejpam-2346	87	4	of	of	ADP
ejpam-2346	87	5	the	the	DET
ejpam-2346	87	6	transformed	transform	VERB
ejpam-2346	87	7	heptahedron	heptahedron	PROPN
ejpam-2346	87	8	h	h	NOUN
ejpam-2346	87	9	′	′	NOUN
ejpam-2346	87	10	are	be	AUX
ejpam-2346	87	11	given	give	VERB
ejpam-2346	87	12	by	by	ADP
ejpam-2346	87	13	h′k	h′k	NOUN
ejpam-2346	87	14	:	:	PUNCT
ejpam-2346	87	15	=	=	SYM
ejpam-2346	87	16	ck	ck	PROPN
ejpam-2346	88	1	+	+	NUM
ejpam-2346	88	2	σ	σ	PROPN
ejpam-2346	88	3	√	√	PROPN
ejpam-2346	88	4	|nk|	|nk|	PROPN
ejpam-2346	88	5	nk	nk	PROPN
ejpam-2346	88	6	,	,	PUNCT
ejpam-2346	88	7	k	k	PROPN
ejpam-2346	88	8	∈	∈	PROPN
ejpam-2346	88	9	{	{	PUNCT
ejpam-2346	88	10	1	1	NUM
ejpam-2346	88	11	,	,	PUNCT
ejpam-2346	88	12	....	....	PUNCT
ejpam-2346	88	13	,	,	PUNCT
ejpam-2346	88	14	7	7	NUM
ejpam-2346	88	15	}	}	PUNCT
ejpam-2346	88	16	.	.	PUNCT
ejpam-2346	89	1	(	(	PUNCT
ejpam-2346	89	2	3	3	X
ejpam-2346	89	3	)	)	PUNCT
ejpam-2346	89	4	that	that	PRON
ejpam-2346	89	5	is	be	AUX
ejpam-2346	89	6	h′k	h′k	NOUN
ejpam-2346	89	7	is	be	AUX
ejpam-2346	89	8	obtained	obtain	VERB
ejpam-2346	89	9	by	by	ADP
ejpam-2346	89	10	adding	add	VERB
ejpam-2346	89	11	the	the	DET
ejpam-2346	89	12	centroid	centroid	NOUN
ejpam-2346	89	13	ck	ck	NOUN
ejpam-2346	89	14	of	of	ADP
ejpam-2346	89	15	the	the	DET
ejpam-2346	89	16	heptahedron	heptahedron	ADJ
ejpam-2346	89	17	face	face	NOUN
ejpam-2346	89	18	with	with	ADP
ejpam-2346	89	19	the	the	DET
ejpam-2346	89	20	associated	associate	VERB
ejpam-2346	89	21	normal	normal	ADJ
ejpam-2346	89	22	nk	nk	PROPN
ejpam-2346	89	23	scaled	scale	VERB
ejpam-2346	89	24	by	by	ADP
ejpam-2346	89	25	σ/	σ/	NOUN
ejpam-2346	89	26	√	√	PROPN
ejpam-2346	89	27	|nk|	|nk|	PROPN
ejpam-2346	89	28	.	.	PUNCT
ejpam-2346	90	1	s.	s.	PROPN
ejpam-2346	90	2	dey	dey	PROPN
ejpam-2346	90	3	,	,	PUNCT
ejpam-2346	90	4	b.	b.	PROPN
ejpam-2346	90	5	pal	pal	PROPN
ejpam-2346	90	6	,	,	PUNCT
ejpam-2346	90	7	a.	a.	NOUN
ejpam-2346	90	8	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	90	9	/	/	SYM
ejpam-2346	90	10	eur	eur	PROPN
ejpam-2346	90	11	.	.	PUNCT
ejpam-2346	91	1	j.	j.	PROPN
ejpam-2346	91	2	pure	pure	PROPN
ejpam-2346	91	3	appl	appl	PROPN
ejpam-2346	91	4	.	.	PROPN
ejpam-2346	91	5	math	math	PROPN
ejpam-2346	91	6	,	,	PUNCT
ejpam-2346	91	7	11	11	NUM
ejpam-2346	91	8	(	(	PUNCT
ejpam-2346	91	9	1	1	NUM
ejpam-2346	91	10	)	)	PUNCT
ejpam-2346	91	11	(	(	PUNCT
ejpam-2346	91	12	2018	2018	NUM
ejpam-2346	91	13	)	)	PUNCT
ejpam-2346	91	14	,	,	PUNCT
ejpam-2346	91	15	315	315	NUM
ejpam-2346	91	16	-	-	SYM
ejpam-2346	91	17	330	330	NUM
ejpam-2346	91	18	319	319	NUM
ejpam-2346	91	19	3.4	3.4	NUM
ejpam-2346	91	20	apex	apex	NOUN
ejpam-2346	91	21	transformation	transformation	NOUN
ejpam-2346	91	22	of	of	ADP
ejpam-2346	91	23	the	the	DET
ejpam-2346	91	24	heptahedron	heptahedron	NOUN
ejpam-2346	91	25	using	use	VERB
ejpam-2346	91	26	centroid	centroid	NOUN
ejpam-2346	91	27	transformation	transformation	NOUN
ejpam-2346	91	28	:	:	PUNCT
ejpam-2346	91	29	in	in	ADP
ejpam-2346	91	30	this	this	DET
ejpam-2346	91	31	case	case	NOUN
ejpam-2346	91	32	we	we	PRON
ejpam-2346	91	33	only	only	ADV
ejpam-2346	91	34	transform	transform	VERB
ejpam-2346	91	35	the	the	DET
ejpam-2346	91	36	apex	apex	NOUN
ejpam-2346	91	37	(	(	PUNCT
ejpam-2346	91	38	top	top	ADJ
ejpam-2346	91	39	vertex	vertex	NOUN
ejpam-2346	91	40	)	)	PUNCT
ejpam-2346	91	41	of	of	ADP
ejpam-2346	91	42	the	the	DET
ejpam-2346	91	43	heptahedron	heptahedron	NOUN
ejpam-2346	91	44	using	use	VERB
ejpam-2346	91	45	method	method	NOUN
ejpam-2346	91	46	(	(	PUNCT
ejpam-2346	91	47	3	3	NUM
ejpam-2346	91	48	)	)	PUNCT
ejpam-2346	91	49	.	.	PUNCT
ejpam-2346	92	1	so	so	ADV
ejpam-2346	92	2	,	,	PUNCT
ejpam-2346	92	3	here	here	ADV
ejpam-2346	92	4	we	we	PRON
ejpam-2346	92	5	transform	transform	VERB
ejpam-2346	92	6	h7	h7	PROPN
ejpam-2346	92	7	to	to	PART
ejpam-2346	92	8	h′7	h′7	VERB
ejpam-2346	92	9	and	and	CCONJ
ejpam-2346	92	10	the	the	DET
ejpam-2346	92	11	transformed	transform	VERB
ejpam-2346	92	12	heptahedron	heptahedron	NOUN
ejpam-2346	92	13	is	be	AUX
ejpam-2346	92	14	given	give	VERB
ejpam-2346	92	15	by	by	ADP
ejpam-2346	92	16	h	h	NOUN
ejpam-2346	92	17	′	′	NUM
ejpam-2346	92	18	=	=	PUNCT
ejpam-2346	92	19			PROPN
ejpam-2346	92	20			NOUN
ejpam-2346	92	21			NOUN
ejpam-2346	92	22			NOUN
ejpam-2346	92	23			NOUN
ejpam-2346	92	24			NOUN
ejpam-2346	92	25			NOUN
ejpam-2346	92	26			NOUN
ejpam-2346	92	27			NOUN
ejpam-2346	92	28			NOUN
ejpam-2346	92	29	h′1	h′1	VERB
ejpam-2346	92	30	h′2	h′2	NOUN
ejpam-2346	93	1	h′3	h′3	PROPN
ejpam-2346	93	2	h′4	h′4	PROPN
ejpam-2346	93	3	h′5	h′5	X
ejpam-2346	94	1	h′6	h′6	PROPN
ejpam-2346	94	2	h′7	h′7	NOUN
ejpam-2346	94	3			PROPN
ejpam-2346	94	4			NOUN
ejpam-2346	94	5			VERB
ejpam-2346	94	6			NOUN
ejpam-2346	94	7			NOUN
ejpam-2346	94	8			NOUN
ejpam-2346	94	9			NOUN
ejpam-2346	94	10			NOUN
ejpam-2346	94	11			NOUN
ejpam-2346	94	12			PUNCT
ejpam-2346	95	1	:	:	PUNCT
ejpam-2346	95	2	=	=	SYM
ejpam-2346	95	3			PROPN
ejpam-2346	95	4			NOUN
ejpam-2346	95	5			NOUN
ejpam-2346	95	6			NOUN
ejpam-2346	95	7			NOUN
ejpam-2346	95	8			NOUN
ejpam-2346	95	9			NOUN
ejpam-2346	95	10			NOUN
ejpam-2346	95	11			NOUN
ejpam-2346	95	12			PROPN
ejpam-2346	95	13	c1	c1	PROPN
ejpam-2346	95	14	c2	c2	PROPN
ejpam-2346	95	15	c3	c3	PROPN
ejpam-2346	95	16	c4	c4	PROPN
ejpam-2346	95	17	c5	c5	PROPN
ejpam-2346	95	18	c6	c6	PROPN
ejpam-2346	95	19	c7	c7	PROPN
ejpam-2346	95	20			PROPN
ejpam-2346	95	21			VERB
ejpam-2346	95	22			VERB
ejpam-2346	95	23			NOUN
ejpam-2346	95	24			NOUN
ejpam-2346	95	25			NOUN
ejpam-2346	95	26			NOUN
ejpam-2346	95	27			NOUN
ejpam-2346	95	28			NOUN
ejpam-2346	95	29			PUNCT
ejpam-2346	96	1	+	+	CCONJ
ejpam-2346	96	2	σ	σ	NUM
ejpam-2346	96	3			PROPN
ejpam-2346	96	4			NOUN
ejpam-2346	96	5			NOUN
ejpam-2346	96	6			NOUN
ejpam-2346	96	7			NOUN
ejpam-2346	96	8			NOUN
ejpam-2346	96	9			NOUN
ejpam-2346	96	10			NOUN
ejpam-2346	96	11			NOUN
ejpam-2346	96	12			NOUN
ejpam-2346	96	13			NOUN
ejpam-2346	96	14	0	0	NUM
ejpam-2346	96	15	0	0	NUM
ejpam-2346	96	16	0	0	NUM
ejpam-2346	96	17	0	0	NUM
ejpam-2346	96	18	0	0	NUM
ejpam-2346	96	19	0	0	NUM
ejpam-2346	96	20	1√	1√	NUM
ejpam-2346	96	21	|n7|	|n7|	NOUN
ejpam-2346	96	22	n7	n7	PROPN
ejpam-2346	96	23			PROPN
ejpam-2346	96	24			NOUN
ejpam-2346	96	25			VERB
ejpam-2346	96	26			NOUN
ejpam-2346	96	27			NOUN
ejpam-2346	96	28			NOUN
ejpam-2346	96	29			NOUN
ejpam-2346	96	30			NOUN
ejpam-2346	96	31			NOUN
ejpam-2346	96	32			NOUN
ejpam-2346	96	33			PUNCT
ejpam-2346	97	1	(	(	PUNCT
ejpam-2346	97	2	4	4	X
ejpam-2346	97	3	)	)	PUNCT
ejpam-2346	97	4	here	here	ADV
ejpam-2346	97	5	ck	ck	INTJ
ejpam-2346	97	6	is	be	AUX
ejpam-2346	97	7	the	the	DET
ejpam-2346	97	8	centroid	centroid	NOUN
ejpam-2346	97	9	of	of	ADP
ejpam-2346	97	10	kth	kth	PROPN
ejpam-2346	97	11	heptahedron	heptahedron	PROPN
ejpam-2346	97	12	face	face	NOUN
ejpam-2346	97	13	where	where	SCONJ
ejpam-2346	97	14	the	the	DET
ejpam-2346	97	15	associated	associated	ADJ
ejpam-2346	97	16	normal	normal	ADJ
ejpam-2346	97	17	nk	nk	PROPN
ejpam-2346	97	18	scaled	scale	VERB
ejpam-2346	97	19	by	by	ADP
ejpam-2346	97	20	σ/	σ/	NOUN
ejpam-2346	97	21	√	√	ADP
ejpam-2346	97	22	|nk|	|nk|	PROPN
ejpam-2346	97	23	,	,	PUNCT
ejpam-2346	97	24	k	k	PROPN
ejpam-2346	97	25	∈	∈	PROPN
ejpam-2346	97	26	{	{	PUNCT
ejpam-2346	97	27	1	1	NUM
ejpam-2346	97	28	,	,	PUNCT
ejpam-2346	97	29	.....	.....	PUNCT
ejpam-2346	97	30	7	7	NUM
ejpam-2346	97	31	}	}	PUNCT
ejpam-2346	97	32	and	and	CCONJ
ejpam-2346	97	33	n7	n7	PROPN
ejpam-2346	97	34	:	:	PUNCT
ejpam-2346	97	35	=	=	SYM
ejpam-2346	97	36	(	(	PUNCT
ejpam-2346	97	37	h5	h5	PROPN
ejpam-2346	97	38	−	−	PROPN
ejpam-2346	97	39	h6)×	h6)×	NOUN
ejpam-2346	97	40	(	(	PUNCT
ejpam-2346	97	41	h1	h1	VERB
ejpam-2346	97	42	−	−	PROPN
ejpam-2346	97	43	h6	h6	PROPN
ejpam-2346	97	44	)	)	PUNCT
ejpam-2346	97	45	of	of	ADP
ejpam-2346	97	46	h.	h.	PROPN
ejpam-2346	97	47	3.5	3.5	NUM
ejpam-2346	97	48	apex	apex	NOUN
ejpam-2346	97	49	transformation	transformation	NOUN
ejpam-2346	97	50	of	of	ADP
ejpam-2346	97	51	the	the	DET
ejpam-2346	97	52	heptahedron	heptahedron	NOUN
ejpam-2346	97	53	using	use	VERB
ejpam-2346	97	54	centroid	centroid	NOUN
ejpam-2346	97	55	transformation	transformation	NOUN
ejpam-2346	97	56	but	but	CCONJ
ejpam-2346	97	57	base	base	NOUN
ejpam-2346	97	58	points	point	NOUN
ejpam-2346	97	59	are	be	AUX
ejpam-2346	97	60	fixed	fix	VERB
ejpam-2346	97	61	:	:	PUNCT
ejpam-2346	97	62	in	in	ADP
ejpam-2346	97	63	this	this	DET
ejpam-2346	97	64	case	case	NOUN
ejpam-2346	97	65	we	we	PRON
ejpam-2346	97	66	transform	transform	VERB
ejpam-2346	97	67	the	the	DET
ejpam-2346	97	68	apex	apex	NOUN
ejpam-2346	97	69	of	of	ADP
ejpam-2346	97	70	the	the	DET
ejpam-2346	97	71	heptahedron	heptahedron	NOUN
ejpam-2346	97	72	using	use	VERB
ejpam-2346	97	73	centroid	centroid	NOUN
ejpam-2346	97	74	transformation	transformation	NOUN
ejpam-2346	97	75	but	but	CCONJ
ejpam-2346	97	76	other	other	ADJ
ejpam-2346	97	77	base	base	NOUN
ejpam-2346	97	78	points	point	NOUN
ejpam-2346	97	79	are	be	AUX
ejpam-2346	97	80	unaltered	unaltere	VERB
ejpam-2346	97	81	.	.	PUNCT
ejpam-2346	98	1	so	so	ADV
ejpam-2346	98	2	,	,	PUNCT
ejpam-2346	98	3	here	here	ADV
ejpam-2346	98	4	only	only	ADV
ejpam-2346	98	5	transform	transform	VERB
ejpam-2346	98	6	h7	h7	PROPN
ejpam-2346	98	7	to	to	PART
ejpam-2346	98	8	h′7	h′7	VERB
ejpam-2346	98	9	and	and	CCONJ
ejpam-2346	98	10	we	we	PRON
ejpam-2346	98	11	define	define	VERB
ejpam-2346	98	12	the	the	DET
ejpam-2346	98	13	heptahedron	heptahedron	NOUN
ejpam-2346	98	14	is	be	AUX
ejpam-2346	98	15	given	give	VERB
ejpam-2346	98	16	by	by	ADP
ejpam-2346	98	17	h	h	NOUN
ejpam-2346	98	18	′	′	NUM
ejpam-2346	98	19	=	=	PUNCT
ejpam-2346	98	20			PROPN
ejpam-2346	98	21			NOUN
ejpam-2346	98	22			NOUN
ejpam-2346	98	23			NOUN
ejpam-2346	98	24			NOUN
ejpam-2346	98	25			NOUN
ejpam-2346	98	26			NOUN
ejpam-2346	98	27			NOUN
ejpam-2346	98	28			NOUN
ejpam-2346	98	29			NOUN
ejpam-2346	98	30	h′1	h′1	VERB
ejpam-2346	99	1	h′2	h′2	NOUN
ejpam-2346	99	2	h′3	h′3	PROPN
ejpam-2346	100	1	h′4	h′4	PROPN
ejpam-2346	100	2	h′5	h′5	X
ejpam-2346	100	3	h′6	h′6	PROPN
ejpam-2346	100	4	h′7	h′7	NOUN
ejpam-2346	100	5			PROPN
ejpam-2346	100	6			NOUN
ejpam-2346	100	7			VERB
ejpam-2346	100	8			NOUN
ejpam-2346	100	9			NOUN
ejpam-2346	100	10			NOUN
ejpam-2346	100	11			NOUN
ejpam-2346	100	12			NOUN
ejpam-2346	100	13			NOUN
ejpam-2346	100	14			PUNCT
ejpam-2346	101	1	:	:	PUNCT
ejpam-2346	101	2	=	=	SYM
ejpam-2346	101	3			PROPN
ejpam-2346	101	4			NOUN
ejpam-2346	101	5			NOUN
ejpam-2346	101	6			NOUN
ejpam-2346	101	7			NOUN
ejpam-2346	101	8			NOUN
ejpam-2346	101	9			NOUN
ejpam-2346	101	10			NOUN
ejpam-2346	101	11			NOUN
ejpam-2346	101	12			NOUN
ejpam-2346	101	13	h1	h1	VERB
ejpam-2346	101	14	h2	h2	PROPN
ejpam-2346	101	15	h3	h3	NOUN
ejpam-2346	101	16	h4	h4	PROPN
ejpam-2346	101	17	h5	h5	PROPN
ejpam-2346	101	18	h6	h6	PROPN
ejpam-2346	101	19	c7	c7	PROPN
ejpam-2346	101	20			PROPN
ejpam-2346	101	21			VERB
ejpam-2346	101	22			VERB
ejpam-2346	101	23			NOUN
ejpam-2346	101	24			NOUN
ejpam-2346	101	25			NOUN
ejpam-2346	101	26			NOUN
ejpam-2346	101	27			NOUN
ejpam-2346	101	28			NOUN
ejpam-2346	101	29			PUNCT
ejpam-2346	102	1	+	+	CCONJ
ejpam-2346	102	2	σ	σ	NUM
ejpam-2346	102	3			PROPN
ejpam-2346	102	4			NOUN
ejpam-2346	102	5			NOUN
ejpam-2346	102	6			NOUN
ejpam-2346	102	7			NOUN
ejpam-2346	102	8			NOUN
ejpam-2346	102	9			NOUN
ejpam-2346	102	10			NOUN
ejpam-2346	102	11			NOUN
ejpam-2346	102	12			NOUN
ejpam-2346	102	13			NOUN
ejpam-2346	102	14	0	0	NUM
ejpam-2346	102	15	0	0	NUM
ejpam-2346	102	16	0	0	NUM
ejpam-2346	102	17	0	0	NUM
ejpam-2346	102	18	0	0	NUM
ejpam-2346	102	19	0	0	NUM
ejpam-2346	102	20	1√	1√	PROPN
ejpam-2346	102	21	|n7|	|n7|	NOUN
ejpam-2346	102	22	n7	n7	PROPN
ejpam-2346	102	23	.	.	PUNCT
ejpam-2346	103	1			PROPN
ejpam-2346	103	2			NOUN
ejpam-2346	103	3			VERB
ejpam-2346	103	4			NOUN
ejpam-2346	103	5			NOUN
ejpam-2346	103	6			NOUN
ejpam-2346	103	7			NOUN
ejpam-2346	103	8			NOUN
ejpam-2346	103	9			NOUN
ejpam-2346	103	10			NOUN
ejpam-2346	103	11			PUNCT
ejpam-2346	104	1	(	(	PUNCT
ejpam-2346	104	2	5	5	X
ejpam-2346	104	3	)	)	PUNCT
ejpam-2346	104	4	s.	s.	PROPN
ejpam-2346	104	5	dey	dey	PROPN
ejpam-2346	104	6	,	,	PUNCT
ejpam-2346	104	7	b.	b.	PROPN
ejpam-2346	104	8	pal	pal	PROPN
ejpam-2346	104	9	,	,	PUNCT
ejpam-2346	104	10	a.	a.	NOUN
ejpam-2346	104	11	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	104	12	/	/	SYM
ejpam-2346	104	13	eur	eur	PROPN
ejpam-2346	104	14	.	.	PUNCT
ejpam-2346	105	1	j.	j.	PROPN
ejpam-2346	105	2	pure	pure	PROPN
ejpam-2346	105	3	appl	appl	PROPN
ejpam-2346	105	4	.	.	PROPN
ejpam-2346	105	5	math	math	PROPN
ejpam-2346	105	6	,	,	PUNCT
ejpam-2346	105	7	11	11	NUM
ejpam-2346	105	8	(	(	PUNCT
ejpam-2346	105	9	1	1	NUM
ejpam-2346	105	10	)	)	PUNCT
ejpam-2346	105	11	(	(	PUNCT
ejpam-2346	105	12	2018	2018	NUM
ejpam-2346	105	13	)	)	PUNCT
ejpam-2346	105	14	,	,	PUNCT
ejpam-2346	105	15	315	315	NUM
ejpam-2346	105	16	-	-	SYM
ejpam-2346	105	17	330	330	NUM
ejpam-2346	105	18	320	320	NUM
ejpam-2346	105	19	in	in	ADP
ejpam-2346	105	20	the	the	DET
ejpam-2346	105	21	following	follow	VERB
ejpam-2346	105	22	figure	figure	NOUN
ejpam-2346	105	23	we	we	PRON
ejpam-2346	105	24	want	want	VERB
ejpam-2346	105	25	to	to	PART
ejpam-2346	105	26	demonstrate	demonstrate	VERB
ejpam-2346	105	27	the	the	DET
ejpam-2346	105	28	method	method	NOUN
ejpam-2346	105	29	(	(	PUNCT
ejpam-2346	105	30	5	5	X
ejpam-2346	105	31	)	)	PUNCT
ejpam-2346	105	32	fig.1	fig.1	PROPN
ejpam-2346	105	33	:	:	PUNCT
ejpam-2346	105	34	before	before	ADP
ejpam-2346	105	35	transformation	transformation	NOUN
ejpam-2346	105	36	of	of	ADP
ejpam-2346	105	37	heptahedron	heptahedron	PROPN
ejpam-2346	105	38	fig.2	fig.2	PROPN
ejpam-2346	105	39	:	:	PUNCT
ejpam-2346	105	40	deformed	deform	VERB
ejpam-2346	105	41	heptahedron	heptahedron	NOUN
ejpam-2346	105	42	4	4	NUM
ejpam-2346	105	43	.	.	PUNCT
ejpam-2346	105	44	properties	property	NOUN
ejpam-2346	105	45	of	of	ADP
ejpam-2346	105	46	transformations	transformation	NOUN
ejpam-2346	105	47	:	:	PUNCT
ejpam-2346	105	48	in	in	ADP
ejpam-2346	105	49	this	this	DET
ejpam-2346	105	50	section	section	NOUN
ejpam-2346	105	51	,	,	PUNCT
ejpam-2346	105	52	we	we	PRON
ejpam-2346	105	53	discuss	discuss	VERB
ejpam-2346	105	54	the	the	DET
ejpam-2346	105	55	basic	basic	ADJ
ejpam-2346	105	56	properties	property	NOUN
ejpam-2346	105	57	of	of	ADP
ejpam-2346	105	58	the	the	DET
ejpam-2346	105	59	above	above	ADJ
ejpam-2346	105	60	four	four	NUM
ejpam-2346	105	61	transformations	transformation	NOUN
ejpam-2346	105	62	.	.	PUNCT
ejpam-2346	106	1	4.1	4.1	NUM
ejpam-2346	106	2	the	the	DET
ejpam-2346	106	3	transformations	transformation	NOUN
ejpam-2346	106	4	are	be	AUX
ejpam-2346	106	5	scale	scale	NOUN
ejpam-2346	106	6	invariant	invariant	ADJ
ejpam-2346	106	7	:	:	PUNCT
ejpam-2346	106	8	proof	proof	NOUN
ejpam-2346	106	9	:	:	PUNCT
ejpam-2346	106	10	since	since	SCONJ
ejpam-2346	106	11	the	the	DET
ejpam-2346	106	12	normals	normal	NOUN
ejpam-2346	106	13	ni	ni	PROPN
ejpam-2346	106	14	are	be	AUX
ejpam-2346	106	15	scaled	scale	VERB
ejpam-2346	106	16	by	by	ADP
ejpam-2346	106	17	1/	1/	NUM
ejpam-2346	106	18	√	√	PROPN
ejpam-2346	106	19	|ni|	|ni|	PROPN
ejpam-2346	106	20	,	,	PUNCT
ejpam-2346	106	21	therefore	therefore	ADV
ejpam-2346	106	22	the	the	DET
ejpam-2346	106	23	transformations	transformation	NOUN
ejpam-2346	106	24	given	give	VERB
ejpam-2346	106	25	by	by	ADP
ejpam-2346	106	26	(	(	PUNCT
ejpam-2346	106	27	1	1	NUM
ejpam-2346	106	28	)	)	PUNCT
ejpam-2346	106	29	,	,	PUNCT
ejpam-2346	106	30	(	(	PUNCT
ejpam-2346	106	31	2	2	NUM
ejpam-2346	106	32	)	)	PUNCT
ejpam-2346	106	33	,	,	PUNCT
ejpam-2346	106	34	(	(	PUNCT
ejpam-2346	106	35	3	3	NUM
ejpam-2346	106	36	)	)	PUNCT
ejpam-2346	106	37	,	,	PUNCT
ejpam-2346	106	38	(	(	PUNCT
ejpam-2346	106	39	4	4	NUM
ejpam-2346	106	40	)	)	PUNCT
ejpam-2346	106	41	,	,	PUNCT
ejpam-2346	106	42	(	(	PUNCT
ejpam-2346	106	43	5	5	X
ejpam-2346	106	44	)	)	PUNCT
ejpam-2346	106	45	are	be	AUX
ejpam-2346	106	46	scale	scale	NOUN
ejpam-2346	106	47	invariant	invariant	ADJ
ejpam-2346	106	48	,	,	PUNCT
ejpam-2346	106	49	that	that	PRON
ejpam-2346	106	50	means	mean	VERB
ejpam-2346	106	51	for	for	ADP
ejpam-2346	106	52	any	any	DET
ejpam-2346	106	53	s	s	X
ejpam-2346	106	54	>	>	X
ejpam-2346	106	55	0	0	NUM
ejpam-2346	106	56	,	,	PUNCT
ejpam-2346	106	57	(	(	PUNCT
ejpam-2346	106	58	sh)′	sh)′	X
ejpam-2346	106	59	=	=	SYM
ejpam-2346	106	60	sh	sh	PROPN
ejpam-2346	106	61	′.	′.	NOUN
ejpam-2346	106	62	to	to	PART
ejpam-2346	106	63	check	check	VERB
ejpam-2346	106	64	this	this	DET
ejpam-2346	106	65	property	property	NOUN
ejpam-2346	106	66	we	we	PRON
ejpam-2346	106	67	shall	shall	AUX
ejpam-2346	106	68	consider	consider	VERB
ejpam-2346	106	69	some	some	DET
ejpam-2346	106	70	examples	example	NOUN
ejpam-2346	106	71	where	where	SCONJ
ejpam-2346	106	72	we	we	PRON
ejpam-2346	106	73	choose	choose	VERB
ejpam-2346	106	74	σ	σ	NOUN
ejpam-2346	106	75	=	=	SYM
ejpam-2346	106	76	0.1	0.1	NUM
ejpam-2346	106	77	.	.	PUNCT
ejpam-2346	106	78	example	example	NOUN
ejpam-2346	107	1	1	1	NUM
ejpam-2346	107	2	.	.	PUNCT
ejpam-2346	107	3	in	in	ADP
ejpam-2346	107	4	this	this	DET
ejpam-2346	107	5	example	example	NOUN
ejpam-2346	107	6	,	,	PUNCT
ejpam-2346	107	7	we	we	PRON
ejpam-2346	107	8	use	use	VERB
ejpam-2346	107	9	the	the	DET
ejpam-2346	107	10	transformations	transformation	NOUN
ejpam-2346	107	11	(	(	PUNCT
ejpam-2346	107	12	1	1	NUM
ejpam-2346	107	13	)	)	PUNCT
ejpam-2346	107	14	and	and	CCONJ
ejpam-2346	107	15	then	then	ADV
ejpam-2346	107	16	investigate	investigate	VERB
ejpam-2346	107	17	the	the	DET
ejpam-2346	107	18	properties	property	NOUN
ejpam-2346	107	19	of	of	ADP
ejpam-2346	107	20	(	(	PUNCT
ejpam-2346	107	21	sh)′	sh)′	X
ejpam-2346	107	22	=	=	SYM
ejpam-2346	107	23	sh	sh	PROPN
ejpam-2346	107	24	′.	′.	NOUN
ejpam-2346	107	25	let	let	VERB
ejpam-2346	107	26	h	h	NOUN
ejpam-2346	107	27	:	:	PUNCT
ejpam-2346	107	28	=	=	SYM
ejpam-2346	107	29	(	(	PUNCT
ejpam-2346	107	30	h1	h1	PROPN
ejpam-2346	107	31	,	,	PUNCT
ejpam-2346	107	32	h2	h2	PROPN
ejpam-2346	107	33	,	,	PUNCT
ejpam-2346	107	34	h3	h3	NOUN
ejpam-2346	107	35	,	,	PUNCT
ejpam-2346	107	36	h4	h4	NOUN
ejpam-2346	107	37	,	,	PUNCT
ejpam-2346	107	38	h5	h5	PROPN
ejpam-2346	107	39	,	,	PUNCT
ejpam-2346	107	40	h6	h6	PROPN
ejpam-2346	107	41	,	,	PUNCT
ejpam-2346	107	42	h7	h7	PROPN
ejpam-2346	107	43	)	)	PUNCT
ejpam-2346	107	44	t	t	PROPN
ejpam-2346	107	45	denote	denote	VERB
ejpam-2346	107	46	the	the	DET
ejpam-2346	107	47	heptahedron	heptahedron	NOUN
ejpam-2346	107	48	with	with	ADP
ejpam-2346	107	49	h1	h1	PROPN
ejpam-2346	107	50	≡	≡	PROPN
ejpam-2346	107	51	(	(	PUNCT
ejpam-2346	107	52	−.64	−.64	PROPN
ejpam-2346	107	53	,	,	PUNCT
ejpam-2346	107	54	.48	.48	NUM
ejpam-2346	107	55	,	,	PUNCT
ejpam-2346	107	56	.6	.6	NUM
ejpam-2346	107	57	)	)	PUNCT
ejpam-2346	107	58	,	,	PUNCT
ejpam-2346	107	59	h2	h2	PROPN
ejpam-2346	107	60	≡	≡	PROPN
ejpam-2346	107	61	(	(	PUNCT
ejpam-2346	107	62	.8	.8	PROPN
ejpam-2346	107	63	,	,	PUNCT
ejpam-2346	107	64	0	0	NUM
ejpam-2346	107	65	,	,	PUNCT
ejpam-2346	107	66	.6	.6	NUM
ejpam-2346	107	67	)	)	PUNCT
ejpam-2346	107	68	,	,	PUNCT
ejpam-2346	107	69	h3	h3	NOUN
ejpam-2346	107	70	≡	≡	PROPN
ejpam-2346	107	71	(	(	PUNCT
ejpam-2346	107	72	0,−.8	0,−.8	PROPN
ejpam-2346	107	73	,	,	PUNCT
ejpam-2346	107	74	.6	.6	NUM
ejpam-2346	107	75	)	)	PUNCT
ejpam-2346	107	76	,	,	PUNCT
ejpam-2346	107	77	h4	h4	PROPN
ejpam-2346	107	78	≡	≡	PROPN
ejpam-2346	107	79	(	(	PUNCT
ejpam-2346	107	80	−.8	−.8	PROPN
ejpam-2346	107	81	,	,	PUNCT
ejpam-2346	107	82	0	0	NUM
ejpam-2346	107	83	,	,	PUNCT
ejpam-2346	107	84	.6	.6	NUM
ejpam-2346	107	85	)	)	PUNCT
ejpam-2346	107	86	,	,	PUNCT
ejpam-2346	107	87	h5	h5	PROPN
ejpam-2346	107	88	≡	≡	PROPN
ejpam-2346	107	89	(	(	PUNCT
ejpam-2346	107	90	0	0	NUM
ejpam-2346	107	91	,	,	PUNCT
ejpam-2346	107	92	.8	.8	NUM
ejpam-2346	107	93	,	,	PUNCT
ejpam-2346	107	94	.6	.6	NUM
ejpam-2346	107	95	)	)	PUNCT
ejpam-2346	107	96	,	,	PUNCT
ejpam-2346	107	97	h6	h6	PROPN
ejpam-2346	107	98	≡	≡	PROPN
ejpam-2346	107	99	(	(	PUNCT
ejpam-2346	107	100	.64,−.48	.64,−.48	PROPN
ejpam-2346	107	101	,	,	PUNCT
ejpam-2346	107	102	.6	.6	NUM
ejpam-2346	107	103	)	)	PUNCT
ejpam-2346	107	104	,	,	PUNCT
ejpam-2346	107	105	h7	h7	PROPN
ejpam-2346	107	106	≡	≡	PROPN
ejpam-2346	107	107	(	(	PUNCT
ejpam-2346	107	108	0	0	NUM
ejpam-2346	107	109	,	,	PUNCT
ejpam-2346	107	110	0	0	NUM
ejpam-2346	107	111	,	,	PUNCT
ejpam-2346	107	112	1	1	NUM
ejpam-2346	107	113	)	)	PUNCT
ejpam-2346	107	114	let	let	VERB
ejpam-2346	107	115	s	s	NOUN
ejpam-2346	107	116	=	=	VERB
ejpam-2346	107	117	0.5	0.5	NUM
ejpam-2346	107	118	and	and	CCONJ
ejpam-2346	107	119	applying	apply	VERB
ejpam-2346	107	120	the	the	DET
ejpam-2346	107	121	transformation	transformation	NOUN
ejpam-2346	107	122	(	(	PUNCT
ejpam-2346	107	123	1	1	X
ejpam-2346	107	124	)	)	PUNCT
ejpam-2346	107	125	both	both	CCONJ
ejpam-2346	107	126	on	on	ADP
ejpam-2346	107	127	(	(	PUNCT
ejpam-2346	107	128	sh)′	sh)′	X
ejpam-2346	107	129	and	and	CCONJ
ejpam-2346	107	130	sh	sh	INTJ
ejpam-2346	107	131	′	′	VERB
ejpam-2346	108	1	after	after	ADP
ejpam-2346	108	2	that	that	PRON
ejpam-2346	108	3	we	we	PRON
ejpam-2346	108	4	get	get	VERB
ejpam-2346	108	5	the	the	DET
ejpam-2346	108	6	following	follow	VERB
ejpam-2346	108	7	table	table	NOUN
ejpam-2346	108	8	s.	s.	PROPN
ejpam-2346	108	9	dey	dey	PROPN
ejpam-2346	108	10	,	,	PUNCT
ejpam-2346	108	11	b.	b.	PROPN
ejpam-2346	108	12	pal	pal	PROPN
ejpam-2346	108	13	,	,	PUNCT
ejpam-2346	108	14	a.	a.	NOUN
ejpam-2346	108	15	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	108	16	/	/	SYM
ejpam-2346	108	17	eur	eur	PROPN
ejpam-2346	108	18	.	.	PUNCT
ejpam-2346	109	1	j.	j.	PROPN
ejpam-2346	109	2	pure	pure	PROPN
ejpam-2346	109	3	appl	appl	PROPN
ejpam-2346	109	4	.	.	PROPN
ejpam-2346	109	5	math	math	PROPN
ejpam-2346	109	6	,	,	PUNCT
ejpam-2346	109	7	11	11	NUM
ejpam-2346	109	8	(	(	PUNCT
ejpam-2346	109	9	1	1	NUM
ejpam-2346	109	10	)	)	PUNCT
ejpam-2346	109	11	(	(	PUNCT
ejpam-2346	109	12	2018	2018	NUM
ejpam-2346	109	13	)	)	PUNCT
ejpam-2346	109	14	,	,	PUNCT
ejpam-2346	109	15	315	315	NUM
ejpam-2346	109	16	-	-	SYM
ejpam-2346	109	17	330	330	NUM
ejpam-2346	109	18	321	321	NUM
ejpam-2346	109	19	vertex	vertex	NOUN
ejpam-2346	109	20	coordinates	coordinate	NOUN
ejpam-2346	109	21	of	of	ADP
ejpam-2346	109	22	(	(	PUNCT
ejpam-2346	109	23	sh)′	sh)′	X
ejpam-2346	109	24	x	x	SYM
ejpam-2346	109	25	y	y	PROPN
ejpam-2346	109	26	z	z	PROPN
ejpam-2346	109	27	(	(	PUNCT
ejpam-2346	109	28	sh1	sh1	PROPN
ejpam-2346	109	29	)	)	PUNCT
ejpam-2346	109	30	′	′	NUM
ejpam-2346	110	1	-.3	-.3	NUM
ejpam-2346	110	2	0.22	0.22	NUM
ejpam-2346	110	3	.34	.34	NUM
ejpam-2346	110	4	(	(	PUNCT
ejpam-2346	110	5	sh2	sh2	PROPN
ejpam-2346	110	6	)	)	PUNCT
ejpam-2346	110	7	′	′	NUM
ejpam-2346	111	1	.38	.38	NUM
ejpam-2346	111	2	-.02	-.02	PROPN
ejpam-2346	112	1	.34	.34	NUM
ejpam-2346	112	2	(	(	PUNCT
ejpam-2346	112	3	sh3	sh3	NOUN
ejpam-2346	112	4	)	)	PUNCT
ejpam-2346	112	5	′	′	NUM
ejpam-2346	113	1	.02	.02	NUM
ejpam-2346	113	2	-.38	-.38	SYM
ejpam-2346	113	3	.34	.34	NUM
ejpam-2346	113	4	(	(	PUNCT
ejpam-2346	113	5	sh4	sh4	NOUN
ejpam-2346	113	6	)	)	PUNCT
ejpam-2346	113	7	′	′	NUM
ejpam-2346	113	8	-.37	-.37	PROPN
ejpam-2346	113	9	.02	.02	NUM
ejpam-2346	113	10	.33	.33	NUM
ejpam-2346	113	11	(	(	PUNCT
ejpam-2346	113	12	sh5	sh5	NOUN
ejpam-2346	113	13	)	)	PUNCT
ejpam-2346	113	14	′	′	NUM
ejpam-2346	113	15	.03	.03	NUM
ejpam-2346	113	16	.44	.44	NUM
ejpam-2346	113	17	.30	.30	NUM
ejpam-2346	113	18	(	(	PUNCT
ejpam-2346	113	19	sh6	sh6	NOUN
ejpam-2346	113	20	)	)	PUNCT
ejpam-2346	113	21	′	′	NUM
ejpam-2346	113	22	.31	.31	NUM
ejpam-2346	113	23	-.28	-.28	SYM
ejpam-2346	113	24	.28	.28	NUM
ejpam-2346	113	25	(	(	PUNCT
ejpam-2346	113	26	sh7	sh7	PROPN
ejpam-2346	113	27	)	)	PUNCT
ejpam-2346	114	1	′	′	NOUN
ejpam-2346	114	2	0	0	NUM
ejpam-2346	114	3	0	0	NUM
ejpam-2346	114	4	.55	.55	NUM
ejpam-2346	114	5	vertex	vertex	NOUN
ejpam-2346	114	6	coordinates	coordinate	NOUN
ejpam-2346	114	7	of	of	ADP
ejpam-2346	114	8	sh	sh	NUM
ejpam-2346	115	1	′	′	NUM
ejpam-2346	115	2	x	x	VERB
ejpam-2346	116	1	y	y	PROPN
ejpam-2346	116	2	z	z	PROPN
ejpam-2346	116	3	sh′1	sh′1	VERB
ejpam-2346	116	4	-.3	-.3	PROPN
ejpam-2346	116	5	0.22	0.22	NUM
ejpam-2346	116	6	.34	.34	NUM
ejpam-2346	116	7	sh′2	sh′2	NOUN
ejpam-2346	116	8	.38	.38	NUM
ejpam-2346	116	9	-.02	-.02	PROPN
ejpam-2346	116	10	.34	.34	NUM
ejpam-2346	116	11	sh′3	sh′3	NOUN
ejpam-2346	116	12	.02	.02	NUM
ejpam-2346	116	13	-.38	-.38	SYM
ejpam-2346	116	14	.34	.34	NUM
ejpam-2346	116	15	sh′4	sh′4	NOUN
ejpam-2346	116	16	-.37	-.37	PROPN
ejpam-2346	116	17	.02	.02	NUM
ejpam-2346	116	18	.33	.33	NUM
ejpam-2346	116	19	sh′5	sh′5	NOUN
ejpam-2346	116	20	.03	.03	NUM
ejpam-2346	116	21	.44	.44	NUM
ejpam-2346	116	22	.30	.30	NUM
ejpam-2346	116	23	sh′6	sh′6	ADJ
ejpam-2346	116	24	.31	.31	NUM
ejpam-2346	116	25	-.28	-.28	SYM
ejpam-2346	116	26	.28	.28	NUM
ejpam-2346	116	27	sh′7	sh′7	NOUN
ejpam-2346	116	28	0	0	NUM
ejpam-2346	116	29	0	0	NUM
ejpam-2346	116	30	.55	.55	NUM
ejpam-2346	116	31	hence	hence	ADV
ejpam-2346	116	32	for	for	ADP
ejpam-2346	116	33	this	this	DET
ejpam-2346	116	34	heptahedron	heptahedron	NOUN
ejpam-2346	116	35	the	the	DET
ejpam-2346	116	36	transformation	transformation	NOUN
ejpam-2346	116	37	(	(	PUNCT
ejpam-2346	116	38	1	1	X
ejpam-2346	116	39	)	)	PUNCT
ejpam-2346	116	40	is	be	AUX
ejpam-2346	116	41	scale	scale	NOUN
ejpam-2346	116	42	invariant	invariant	ADJ
ejpam-2346	116	43	.	.	PUNCT
ejpam-2346	117	1	similarly	similarly	ADV
ejpam-2346	117	2	,	,	PUNCT
ejpam-2346	117	3	we	we	PRON
ejpam-2346	117	4	can	can	AUX
ejpam-2346	117	5	show	show	VERB
ejpam-2346	117	6	that	that	SCONJ
ejpam-2346	117	7	the	the	DET
ejpam-2346	117	8	transformation	transformation	NOUN
ejpam-2346	117	9	(	(	PUNCT
ejpam-2346	117	10	2	2	X
ejpam-2346	117	11	)	)	PUNCT
ejpam-2346	117	12	is	be	AUX
ejpam-2346	117	13	also	also	ADV
ejpam-2346	117	14	scale	scale	ADJ
ejpam-2346	117	15	invariant	invariant	ADJ
ejpam-2346	117	16	.	.	PUNCT
ejpam-2346	117	17	example	example	NOUN
ejpam-2346	118	1	2	2	NUM
ejpam-2346	118	2	.	.	X
ejpam-2346	118	3	in	in	ADP
ejpam-2346	118	4	this	this	DET
ejpam-2346	118	5	example	example	NOUN
ejpam-2346	118	6	,	,	PUNCT
ejpam-2346	118	7	we	we	PRON
ejpam-2346	118	8	use	use	VERB
ejpam-2346	118	9	the	the	DET
ejpam-2346	118	10	transformation	transformation	NOUN
ejpam-2346	118	11	(	(	PUNCT
ejpam-2346	118	12	3	3	NUM
ejpam-2346	118	13	)	)	PUNCT
ejpam-2346	118	14	and	and	CCONJ
ejpam-2346	118	15	then	then	ADV
ejpam-2346	118	16	try	try	VERB
ejpam-2346	118	17	to	to	PART
ejpam-2346	118	18	investigate	investigate	VERB
ejpam-2346	118	19	the	the	DET
ejpam-2346	118	20	property	property	NOUN
ejpam-2346	118	21	of	of	ADP
ejpam-2346	118	22	(	(	PUNCT
ejpam-2346	118	23	sh)′	sh)′	X
ejpam-2346	118	24	=	=	SYM
ejpam-2346	118	25	sh	sh	PROPN
ejpam-2346	118	26	′.	′.	NOUN
ejpam-2346	118	27	we	we	PRON
ejpam-2346	118	28	use	use	VERB
ejpam-2346	118	29	the	the	DET
ejpam-2346	118	30	same	same	ADJ
ejpam-2346	118	31	heptahedron	heptahedron	NOUN
ejpam-2346	118	32	which	which	PRON
ejpam-2346	118	33	is	be	AUX
ejpam-2346	118	34	used	use	VERB
ejpam-2346	118	35	in	in	ADP
ejpam-2346	118	36	example	example	NOUN
ejpam-2346	118	37	(	(	PUNCT
ejpam-2346	118	38	1	1	X
ejpam-2346	118	39	)	)	PUNCT
ejpam-2346	118	40	with	with	ADP
ejpam-2346	118	41	s	s	NOUN
ejpam-2346	118	42	=	=	SYM
ejpam-2346	118	43	0.5	0.5	NUM
ejpam-2346	118	44	and	and	CCONJ
ejpam-2346	118	45	then	then	ADV
ejpam-2346	118	46	applying	apply	VERB
ejpam-2346	118	47	the	the	DET
ejpam-2346	118	48	transformation	transformation	NOUN
ejpam-2346	118	49	(	(	PUNCT
ejpam-2346	118	50	3	3	X
ejpam-2346	118	51	)	)	PUNCT
ejpam-2346	118	52	both	both	PRON
ejpam-2346	118	53	on	on	ADP
ejpam-2346	118	54	(	(	PUNCT
ejpam-2346	118	55	sh)′	sh)′	X
ejpam-2346	118	56	and	and	CCONJ
ejpam-2346	118	57	sh	sh	INTJ
ejpam-2346	118	58	′	′	NOUN
ejpam-2346	119	1	and	and	CCONJ
ejpam-2346	119	2	after	after	ADP
ejpam-2346	119	3	calculations	calculation	NOUN
ejpam-2346	119	4	we	we	PRON
ejpam-2346	119	5	get	get	VERB
ejpam-2346	119	6	the	the	DET
ejpam-2346	119	7	following	follow	VERB
ejpam-2346	119	8	table	table	NOUN
ejpam-2346	119	9	vertex	vertex	NOUN
ejpam-2346	119	10	coordinates	coordinate	NOUN
ejpam-2346	119	11	of	of	ADP
ejpam-2346	119	12	(	(	PUNCT
ejpam-2346	119	13	sh)′	sh)′	X
ejpam-2346	119	14	x	x	SYM
ejpam-2346	119	15	y	y	PROPN
ejpam-2346	119	16	z	z	PROPN
ejpam-2346	119	17	(	(	PUNCT
ejpam-2346	119	18	sh1	sh1	PROPN
ejpam-2346	119	19	)	)	PUNCT
ejpam-2346	119	20	′	′	NUM
ejpam-2346	120	1	.15	.15	NUM
ejpam-2346	120	2	-.15	-.15	NUM
ejpam-2346	120	3	.40	.40	NUM
ejpam-2346	120	4	(	(	PUNCT
ejpam-2346	120	5	sh2	sh2	PROPN
ejpam-2346	120	6	)	)	PUNCT
ejpam-2346	120	7	′	′	NOUN
ejpam-2346	121	1	-.15	-.15	PUNCT
ejpam-2346	121	2	-.15	-.15	PROPN
ejpam-2346	121	3	.40	.40	NUM
ejpam-2346	121	4	(	(	PUNCT
ejpam-2346	121	5	sh3	sh3	NOUN
ejpam-2346	121	6	)	)	PUNCT
ejpam-2346	121	7	′	′	NUM
ejpam-2346	122	1	-.11	-.11	SYM
ejpam-2346	122	2	.15	.15	NUM
ejpam-2346	122	3	.40	.40	NUM
ejpam-2346	122	4	(	(	PUNCT
ejpam-2346	122	5	sh4	sh4	PROPN
ejpam-2346	122	6	)	)	PUNCT
ejpam-2346	122	7	′	′	NUM
ejpam-2346	123	1	.13	.13	NUM
ejpam-2346	123	2	.07	.07	NUM
ejpam-2346	123	3	.39	.39	NUM
ejpam-2346	123	4	(	(	PUNCT
ejpam-2346	123	5	sh5	sh5	NOUN
ejpam-2346	123	6	)	)	PUNCT
ejpam-2346	123	7	′	′	NUM
ejpam-2346	123	8	.03	.03	NUM
ejpam-2346	123	9	.04	.04	NUM
ejpam-2346	123	10	.37	.37	NUM
ejpam-2346	123	11	(	(	PUNCT
ejpam-2346	123	12	sh6	sh6	NOUN
ejpam-2346	123	13	)	)	PUNCT
ejpam-2346	123	14	′	′	NOUN
ejpam-2346	123	15	.01	.01	NUM
ejpam-2346	123	16	.40	.40	NUM
ejpam-2346	123	17	.36	.36	NUM
ejpam-2346	123	18	(	(	PUNCT
ejpam-2346	123	19	sh7	sh7	NOUN
ejpam-2346	123	20	)	)	PUNCT
ejpam-2346	123	21	′	′	NUM
ejpam-2346	123	22	0	0	NUM
ejpam-2346	124	1	.0	.0	NUM
ejpam-2346	124	2	.85	.85	NUM
ejpam-2346	124	3	vertex	vertex	NOUN
ejpam-2346	124	4	coordinates	coordinate	NOUN
ejpam-2346	124	5	of	of	ADP
ejpam-2346	124	6	sh	sh	NUM
ejpam-2346	124	7	′	′	NUM
ejpam-2346	124	8	x	x	VERB
ejpam-2346	125	1	y	y	PROPN
ejpam-2346	125	2	z	z	PROPN
ejpam-2346	125	3	sh′1	sh′1	VERB
ejpam-2346	125	4	.15	.15	NUM
ejpam-2346	125	5	-.15	-.15	PROPN
ejpam-2346	125	6	.40	.40	NUM
ejpam-2346	125	7	sh′2	sh′2	PROPN
ejpam-2346	125	8	-.15	-.15	PROPN
ejpam-2346	125	9	-.15	-.15	PROPN
ejpam-2346	125	10	.40	.40	NUM
ejpam-2346	125	11	sh′3	sh′3	NOUN
ejpam-2346	125	12	-.11	-.11	PUNCT
ejpam-2346	125	13	.15	.15	NUM
ejpam-2346	125	14	.40	.40	NUM
ejpam-2346	125	15	sh′4	sh′4	NOUN
ejpam-2346	125	16	.13	.13	NUM
ejpam-2346	125	17	.07	.07	NUM
ejpam-2346	125	18	.39	.39	NUM
ejpam-2346	125	19	sh′5	sh′5	NOUN
ejpam-2346	125	20	.03	.03	NUM
ejpam-2346	125	21	.04	.04	NUM
ejpam-2346	125	22	.37	.37	NUM
ejpam-2346	125	23	sh′6	sh′6	ADJ
ejpam-2346	125	24	.01	.01	NUM
ejpam-2346	125	25	.40	.40	NUM
ejpam-2346	125	26	.36	.36	NUM
ejpam-2346	125	27	sh′7	sh′7	NOUN
ejpam-2346	125	28	0	0	NUM
ejpam-2346	125	29	.0	.0	NUM
ejpam-2346	125	30	.85	.85	NUM
ejpam-2346	125	31	hence	hence	ADV
ejpam-2346	125	32	for	for	ADP
ejpam-2346	125	33	this	this	DET
ejpam-2346	125	34	heptahedron	heptahedron	NOUN
ejpam-2346	125	35	the	the	DET
ejpam-2346	125	36	transformation	transformation	NOUN
ejpam-2346	125	37	(	(	PUNCT
ejpam-2346	125	38	3	3	X
ejpam-2346	125	39	)	)	PUNCT
ejpam-2346	125	40	is	be	AUX
ejpam-2346	125	41	scale	scale	NOUN
ejpam-2346	125	42	invariant	invariant	ADJ
ejpam-2346	125	43	.	.	PUNCT
ejpam-2346	126	1	one	one	NUM
ejpam-2346	126	2	can	can	AUX
ejpam-2346	126	3	also	also	ADV
ejpam-2346	126	4	show	show	VERB
ejpam-2346	126	5	that	that	SCONJ
ejpam-2346	126	6	the	the	DET
ejpam-2346	126	7	transformation	transformation	NOUN
ejpam-2346	126	8	(	(	PUNCT
ejpam-2346	126	9	4	4	X
ejpam-2346	126	10	)	)	PUNCT
ejpam-2346	126	11	is	be	AUX
ejpam-2346	126	12	also	also	ADV
ejpam-2346	126	13	scale	scale	ADJ
ejpam-2346	126	14	invariant	invariant	ADJ
ejpam-2346	126	15	.	.	PUNCT
ejpam-2346	126	16	example	example	NOUN
ejpam-2346	127	1	3	3	NUM
ejpam-2346	127	2	.	.	PUNCT
ejpam-2346	127	3	in	in	ADP
ejpam-2346	127	4	this	this	DET
ejpam-2346	127	5	example	example	NOUN
ejpam-2346	127	6	,	,	PUNCT
ejpam-2346	127	7	we	we	PRON
ejpam-2346	127	8	use	use	VERB
ejpam-2346	127	9	the	the	DET
ejpam-2346	127	10	transformation	transformation	NOUN
ejpam-2346	127	11	(	(	PUNCT
ejpam-2346	127	12	5	5	NUM
ejpam-2346	127	13	)	)	PUNCT
ejpam-2346	127	14	and	and	CCONJ
ejpam-2346	127	15	then	then	ADV
ejpam-2346	127	16	try	try	VERB
ejpam-2346	127	17	to	to	PART
ejpam-2346	127	18	investigate	investigate	VERB
ejpam-2346	127	19	the	the	DET
ejpam-2346	127	20	property	property	NOUN
ejpam-2346	127	21	of	of	ADP
ejpam-2346	127	22	(	(	PUNCT
ejpam-2346	127	23	sh)′	sh)′	X
ejpam-2346	127	24	=	=	SYM
ejpam-2346	127	25	sh	sh	PROPN
ejpam-2346	127	26	′.	′.	NOUN
ejpam-2346	127	27	we	we	PRON
ejpam-2346	127	28	use	use	VERB
ejpam-2346	127	29	the	the	DET
ejpam-2346	127	30	same	same	ADJ
ejpam-2346	127	31	heptahedron	heptahedron	NOUN
ejpam-2346	127	32	which	which	PRON
ejpam-2346	127	33	is	be	AUX
ejpam-2346	127	34	used	use	VERB
ejpam-2346	127	35	in	in	ADP
ejpam-2346	127	36	example	example	NOUN
ejpam-2346	127	37	(	(	PUNCT
ejpam-2346	127	38	1	1	X
ejpam-2346	127	39	)	)	PUNCT
ejpam-2346	127	40	with	with	ADP
ejpam-2346	127	41	s	s	NOUN
ejpam-2346	127	42	=	=	SYM
ejpam-2346	127	43	0.5	0.5	NUM
ejpam-2346	127	44	and	and	CCONJ
ejpam-2346	127	45	then	then	ADV
ejpam-2346	127	46	applying	apply	VERB
ejpam-2346	127	47	the	the	DET
ejpam-2346	127	48	transformation	transformation	NOUN
ejpam-2346	127	49	(	(	PUNCT
ejpam-2346	127	50	5	5	NUM
ejpam-2346	127	51	)	)	PUNCT
ejpam-2346	127	52	both	both	PRON
ejpam-2346	127	53	on	on	ADP
ejpam-2346	127	54	(	(	PUNCT
ejpam-2346	127	55	sh)′	sh)′	X
ejpam-2346	127	56	and	and	CCONJ
ejpam-2346	127	57	sh	sh	INTJ
ejpam-2346	127	58	′	′	NOUN
ejpam-2346	128	1	and	and	CCONJ
ejpam-2346	128	2	after	after	ADP
ejpam-2346	128	3	calculations	calculation	NOUN
ejpam-2346	128	4	we	we	PRON
ejpam-2346	128	5	get	get	VERB
ejpam-2346	128	6	the	the	DET
ejpam-2346	128	7	following	follow	VERB
ejpam-2346	128	8	table	table	NOUN
ejpam-2346	128	9	s.	s.	PROPN
ejpam-2346	128	10	dey	dey	PROPN
ejpam-2346	128	11	,	,	PUNCT
ejpam-2346	128	12	b.	b.	PROPN
ejpam-2346	128	13	pal	pal	PROPN
ejpam-2346	128	14	,	,	PUNCT
ejpam-2346	128	15	a.	a.	NOUN
ejpam-2346	128	16	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	128	17	/	/	SYM
ejpam-2346	128	18	eur	eur	PROPN
ejpam-2346	128	19	.	.	PUNCT
ejpam-2346	129	1	j.	j.	PROPN
ejpam-2346	129	2	pure	pure	PROPN
ejpam-2346	129	3	appl	appl	PROPN
ejpam-2346	129	4	.	.	PROPN
ejpam-2346	129	5	math	math	PROPN
ejpam-2346	129	6	,	,	PUNCT
ejpam-2346	129	7	11	11	NUM
ejpam-2346	129	8	(	(	PUNCT
ejpam-2346	129	9	1	1	NUM
ejpam-2346	129	10	)	)	PUNCT
ejpam-2346	129	11	(	(	PUNCT
ejpam-2346	129	12	2018	2018	NUM
ejpam-2346	129	13	)	)	PUNCT
ejpam-2346	129	14	,	,	PUNCT
ejpam-2346	129	15	315	315	NUM
ejpam-2346	129	16	-	-	SYM
ejpam-2346	129	17	330	330	NUM
ejpam-2346	129	18	322	322	NUM
ejpam-2346	129	19	vertex	vertex	NOUN
ejpam-2346	129	20	coordinates	coordinate	NOUN
ejpam-2346	129	21	of	of	ADP
ejpam-2346	129	22	(	(	PUNCT
ejpam-2346	129	23	sh)′	sh)′	X
ejpam-2346	129	24	x	x	SYM
ejpam-2346	129	25	y	y	PROPN
ejpam-2346	129	26	z	z	PROPN
ejpam-2346	129	27	(	(	PUNCT
ejpam-2346	129	28	sh1	sh1	PROPN
ejpam-2346	129	29	)	)	PUNCT
ejpam-2346	129	30	′	′	NUM
ejpam-2346	129	31	-.32	-.32	PUNCT
ejpam-2346	129	32	0.24	0.24	NUM
ejpam-2346	129	33	.3	.3	NUM
ejpam-2346	129	34	(	(	PUNCT
ejpam-2346	129	35	sh2	sh2	PROPN
ejpam-2346	129	36	)	)	PUNCT
ejpam-2346	129	37	′	′	NUM
ejpam-2346	130	1	.4	.4	NUM
ejpam-2346	130	2	0	0	NUM
ejpam-2346	130	3	.3	.3	NUM
ejpam-2346	130	4	(	(	PUNCT
ejpam-2346	130	5	sh3	sh3	NOUN
ejpam-2346	130	6	)	)	PUNCT
ejpam-2346	131	1	′	′	NUM
ejpam-2346	131	2	0	0	NUM
ejpam-2346	132	1	-.4	-.4	NUM
ejpam-2346	132	2	.3	.3	NUM
ejpam-2346	132	3	(	(	PUNCT
ejpam-2346	132	4	sh4	sh4	NOUN
ejpam-2346	132	5	)	)	PUNCT
ejpam-2346	132	6	′	′	NUM
ejpam-2346	133	1	-.4	-.4	NUM
ejpam-2346	133	2	0	0	NUM
ejpam-2346	133	3	.3	.3	NUM
ejpam-2346	133	4	(	(	PUNCT
ejpam-2346	133	5	sh5	sh5	NOUN
ejpam-2346	133	6	)	)	PUNCT
ejpam-2346	133	7	′	′	NUM
ejpam-2346	133	8	0	0	NUM
ejpam-2346	134	1	.4	.4	NUM
ejpam-2346	134	2	.3	.3	NUM
ejpam-2346	134	3	(	(	PUNCT
ejpam-2346	134	4	sh6	sh6	NOUN
ejpam-2346	134	5	)	)	PUNCT
ejpam-2346	134	6	′	′	NUM
ejpam-2346	135	1	.32	.32	NUM
ejpam-2346	135	2	-.24	-.24	SYM
ejpam-2346	135	3	.3	.3	NUM
ejpam-2346	135	4	(	(	PUNCT
ejpam-2346	135	5	sh7	sh7	PROPN
ejpam-2346	135	6	)	)	PUNCT
ejpam-2346	135	7	′	′	NOUN
ejpam-2346	135	8	0	0	NUM
ejpam-2346	135	9	0	0	NUM
ejpam-2346	135	10	.85	.85	NUM
ejpam-2346	135	11	vertex	vertex	NOUN
ejpam-2346	135	12	coordinates	coordinate	NOUN
ejpam-2346	135	13	of	of	ADP
ejpam-2346	135	14	sh	sh	NUM
ejpam-2346	135	15	′	′	NUM
ejpam-2346	135	16	x	x	PUNCT
ejpam-2346	136	1	y	y	PROPN
ejpam-2346	136	2	z	z	NOUN
ejpam-2346	136	3	sh′1	sh′1	NOUN
ejpam-2346	136	4	-.32	-.32	PUNCT
ejpam-2346	136	5	0.24	0.24	NUM
ejpam-2346	136	6	.3	.3	NUM
ejpam-2346	136	7	sh′2	sh′2	NOUN
ejpam-2346	136	8	.4	.4	NUM
ejpam-2346	136	9	0	0	NUM
ejpam-2346	136	10	.3	.3	NUM
ejpam-2346	136	11	sh′3	sh′3	NOUN
ejpam-2346	136	12	0	0	NUM
ejpam-2346	137	1	-.4	-.4	NUM
ejpam-2346	137	2	.3	.3	NUM
ejpam-2346	137	3	sh′4	sh′4	NOUN
ejpam-2346	137	4	-.4	-.4	NUM
ejpam-2346	137	5	0	0	NUM
ejpam-2346	137	6	.3	.3	NUM
ejpam-2346	137	7	sh′5	sh′5	NOUN
ejpam-2346	137	8	0	0	NUM
ejpam-2346	138	1	.4	.4	NUM
ejpam-2346	138	2	.3	.3	NUM
ejpam-2346	138	3	sh′6	sh′6	ADJ
ejpam-2346	138	4	.32	.32	NUM
ejpam-2346	138	5	-.24	-.24	SYM
ejpam-2346	138	6	.3	.3	NUM
ejpam-2346	138	7	sh′7	sh′7	NOUN
ejpam-2346	138	8	0	0	NUM
ejpam-2346	138	9	0	0	NUM
ejpam-2346	138	10	.85	.85	NUM
ejpam-2346	138	11	hence	hence	ADV
ejpam-2346	138	12	for	for	ADP
ejpam-2346	138	13	this	this	DET
ejpam-2346	138	14	heptahedron	heptahedron	NOUN
ejpam-2346	138	15	the	the	DET
ejpam-2346	138	16	transformation	transformation	NOUN
ejpam-2346	138	17	(	(	PUNCT
ejpam-2346	138	18	5	5	X
ejpam-2346	138	19	)	)	PUNCT
ejpam-2346	138	20	is	be	AUX
ejpam-2346	138	21	scale	scale	NOUN
ejpam-2346	138	22	invariant	invariant	ADJ
ejpam-2346	138	23	.	.	PUNCT
ejpam-2346	139	1	4.2	4.2	NUM
ejpam-2346	139	2	transformations	transformation	NOUN
ejpam-2346	139	3	(	(	PUNCT
ejpam-2346	139	4	1	1	NUM
ejpam-2346	139	5	)	)	PUNCT
ejpam-2346	139	6	,	,	PUNCT
ejpam-2346	139	7	(	(	PUNCT
ejpam-2346	139	8	2	2	NUM
ejpam-2346	139	9	)	)	PUNCT
ejpam-2346	139	10	,	,	PUNCT
ejpam-2346	139	11	(	(	PUNCT
ejpam-2346	139	12	3	3	NUM
ejpam-2346	139	13	)	)	PUNCT
ejpam-2346	139	14	,	,	PUNCT
ejpam-2346	139	15	(	(	PUNCT
ejpam-2346	139	16	4	4	NUM
ejpam-2346	139	17	)	)	PUNCT
ejpam-2346	139	18	and	and	CCONJ
ejpam-2346	139	19	(	(	PUNCT
ejpam-2346	139	20	5	5	X
ejpam-2346	139	21	)	)	PUNCT
ejpam-2346	139	22	do	do	AUX
ejpam-2346	139	23	not	not	PART
ejpam-2346	139	24	preserve	preserve	VERB
ejpam-2346	139	25	the	the	DET
ejpam-2346	139	26	centroid	centroid	NOUN
ejpam-2346	139	27	of	of	ADP
ejpam-2346	139	28	the	the	DET
ejpam-2346	139	29	heptahedron	heptahedron	NOUN
ejpam-2346	139	30	:	:	PUNCT
ejpam-2346	140	1	proof	proof	NOUN
ejpam-2346	140	2	:	:	PUNCT
ejpam-2346	140	3	the	the	DET
ejpam-2346	140	4	transformations	transformation	NOUN
ejpam-2346	140	5	given	give	VERB
ejpam-2346	140	6	by	by	ADP
ejpam-2346	140	7	(	(	PUNCT
ejpam-2346	140	8	1	1	NUM
ejpam-2346	140	9	)	)	PUNCT
ejpam-2346	140	10	,	,	PUNCT
ejpam-2346	140	11	(	(	PUNCT
ejpam-2346	140	12	2	2	NUM
ejpam-2346	140	13	)	)	PUNCT
ejpam-2346	140	14	,	,	PUNCT
ejpam-2346	140	15	(	(	PUNCT
ejpam-2346	140	16	3	3	NUM
ejpam-2346	140	17	)	)	PUNCT
ejpam-2346	140	18	,	,	PUNCT
ejpam-2346	140	19	(	(	PUNCT
ejpam-2346	140	20	4	4	NUM
ejpam-2346	140	21	)	)	PUNCT
ejpam-2346	140	22	and	and	CCONJ
ejpam-2346	140	23	(	(	PUNCT
ejpam-2346	140	24	5	5	X
ejpam-2346	140	25	)	)	PUNCT
ejpam-2346	140	26	do	do	AUX
ejpam-2346	140	27	not	not	PART
ejpam-2346	140	28	preserve	preserve	VERB
ejpam-2346	140	29	the	the	DET
ejpam-2346	140	30	centroid	centroid	NOUN
ejpam-2346	140	31	of	of	ADP
ejpam-2346	140	32	the	the	DET
ejpam-2346	140	33	heptahedron	heptahedron	NOUN
ejpam-2346	140	34	,	,	PUNCT
ejpam-2346	140	35	that	that	PRON
ejpam-2346	140	36	is	be	AUX
ejpam-2346	140	37	1	1	NUM
ejpam-2346	140	38	7	7	NUM
ejpam-2346	140	39	∑7	∑7	PROPN
ejpam-2346	140	40	i=1	i=1	PROPN
ejpam-2346	140	41	hi	hi	PROPN
ejpam-2346	141	1	6=	6=	NUM
ejpam-2346	141	2	1	1	NUM
ejpam-2346	141	3	7	7	NUM
ejpam-2346	141	4	∑7	∑7	PROPN
ejpam-2346	141	5	i=1	i=1	PROPN
ejpam-2346	141	6	h	h	NOUN
ejpam-2346	141	7	′	′	NUM
ejpam-2346	142	1	i	i	PRON
ejpam-2346	142	2	,	,	PUNCT
ejpam-2346	142	3	where	where	SCONJ
ejpam-2346	142	4	h1	h1	PROPN
ejpam-2346	142	5	,	,	PUNCT
ejpam-2346	142	6	h2	h2	PROPN
ejpam-2346	142	7	,	,	PUNCT
ejpam-2346	142	8	h3	h3	NOUN
ejpam-2346	142	9	,	,	PUNCT
ejpam-2346	142	10	h4	h4	NOUN
ejpam-2346	142	11	,	,	PUNCT
ejpam-2346	142	12	h5	h5	PROPN
ejpam-2346	142	13	,	,	PUNCT
ejpam-2346	142	14	h6	h6	PROPN
ejpam-2346	142	15	,	,	PUNCT
ejpam-2346	142	16	h7	h7	PROPN
ejpam-2346	142	17	are	be	AUX
ejpam-2346	142	18	the	the	DET
ejpam-2346	142	19	vertex	vertex	NOUN
ejpam-2346	142	20	coordinates	coordinate	NOUN
ejpam-2346	142	21	of	of	ADP
ejpam-2346	142	22	original	original	ADJ
ejpam-2346	142	23	heptahedron	heptahedron	NOUN
ejpam-2346	142	24	and	and	CCONJ
ejpam-2346	142	25	h′1	h′1	NOUN
ejpam-2346	142	26	,	,	PUNCT
ejpam-2346	142	27	h	h	NOUN
ejpam-2346	142	28	′	′	NOUN
ejpam-2346	142	29	2	2	NUM
ejpam-2346	142	30	,	,	PUNCT
ejpam-2346	142	31	h	h	NOUN
ejpam-2346	142	32	′	′	NOUN
ejpam-2346	142	33	3	3	NUM
ejpam-2346	142	34	,	,	PUNCT
ejpam-2346	142	35	h	h	NOUN
ejpam-2346	143	1	′	′	NOUN
ejpam-2346	143	2	4	4	NUM
ejpam-2346	143	3	,	,	PUNCT
ejpam-2346	143	4	h	h	NOUN
ejpam-2346	143	5	′	′	NOUN
ejpam-2346	143	6	5	5	NUM
ejpam-2346	143	7	,	,	PUNCT
ejpam-2346	143	8	h	h	NOUN
ejpam-2346	144	1	′	′	NOUN
ejpam-2346	144	2	6	6	NUM
ejpam-2346	144	3	,	,	PUNCT
ejpam-2346	144	4	h	h	NOUN
ejpam-2346	144	5	′	′	NOUN
ejpam-2346	144	6	7	7	NUM
ejpam-2346	144	7	are	be	AUX
ejpam-2346	144	8	the	the	DET
ejpam-2346	144	9	vertex	vertex	NOUN
ejpam-2346	144	10	coordinates	coordinate	NOUN
ejpam-2346	144	11	of	of	ADP
ejpam-2346	144	12	the	the	DET
ejpam-2346	144	13	transformed	transform	VERB
ejpam-2346	144	14	heptahedron	heptahedron	NOUN
ejpam-2346	144	15	.	.	PUNCT
ejpam-2346	145	1	as	as	SCONJ
ejpam-2346	145	2	the	the	DET
ejpam-2346	145	3	scale	scale	NOUN
ejpam-2346	145	4	normals	normal	VERB
ejpam-2346	145	5	ni/	ni/	NOUN
ejpam-2346	145	6	√	√	NUM
ejpam-2346	145	7	|ni|	|ni|	PRON
ejpam-2346	145	8	have	have	AUX
ejpam-2346	145	9	been	be	AUX
ejpam-2346	145	10	used	use	VERB
ejpam-2346	145	11	to	to	PART
ejpam-2346	145	12	ensure	ensure	VERB
ejpam-2346	145	13	the	the	DET
ejpam-2346	145	14	scale	scale	NOUN
ejpam-2346	145	15	invariance	invariance	NOUN
ejpam-2346	145	16	of	of	ADP
ejpam-2346	145	17	the	the	DET
ejpam-2346	145	18	transformation	transformation	NOUN
ejpam-2346	145	19	,	,	PUNCT
ejpam-2346	145	20	so	so	CCONJ
ejpam-2346	145	21	the	the	DET
ejpam-2346	145	22	transformations	transformation	NOUN
ejpam-2346	145	23	(	(	PUNCT
ejpam-2346	145	24	1	1	NUM
ejpam-2346	145	25	)	)	PUNCT
ejpam-2346	145	26	,	,	PUNCT
ejpam-2346	145	27	(	(	PUNCT
ejpam-2346	145	28	2	2	NUM
ejpam-2346	145	29	)	)	PUNCT
ejpam-2346	145	30	,	,	PUNCT
ejpam-2346	145	31	(	(	PUNCT
ejpam-2346	145	32	3	3	NUM
ejpam-2346	145	33	)	)	PUNCT
ejpam-2346	145	34	,	,	PUNCT
ejpam-2346	145	35	(	(	PUNCT
ejpam-2346	145	36	4	4	NUM
ejpam-2346	145	37	)	)	PUNCT
ejpam-2346	145	38	and	and	CCONJ
ejpam-2346	145	39	(	(	PUNCT
ejpam-2346	145	40	5	5	X
ejpam-2346	145	41	)	)	PUNCT
ejpam-2346	145	42	do	do	AUX
ejpam-2346	145	43	not	not	PART
ejpam-2346	145	44	preserve	preserve	VERB
ejpam-2346	145	45	the	the	DET
ejpam-2346	145	46	centroid	centroid	NOUN
ejpam-2346	145	47	of	of	ADP
ejpam-2346	145	48	the	the	DET
ejpam-2346	145	49	heptahedron	heptahedron	NOUN
ejpam-2346	145	50	.	.	PUNCT
ejpam-2346	146	1	we	we	PRON
ejpam-2346	146	2	verify	verify	VERB
ejpam-2346	146	3	it	it	PRON
ejpam-2346	146	4	by	by	ADP
ejpam-2346	146	5	an	an	DET
ejpam-2346	146	6	examples	example	NOUN
ejpam-2346	146	7	.	.	PUNCT
ejpam-2346	147	1	example	example	NOUN
ejpam-2346	148	1	4	4	X
ejpam-2346	148	2	.	.	PUNCT
ejpam-2346	149	1	let	let	VERB
ejpam-2346	149	2	(	(	PUNCT
ejpam-2346	149	3	h1	h1	PROPN
ejpam-2346	149	4	,	,	PUNCT
ejpam-2346	149	5	h2	h2	PROPN
ejpam-2346	149	6	,	,	PUNCT
ejpam-2346	149	7	h3	h3	NOUN
ejpam-2346	149	8	,	,	PUNCT
ejpam-2346	149	9	h4	h4	NOUN
ejpam-2346	149	10	,	,	PUNCT
ejpam-2346	149	11	h5	h5	PROPN
ejpam-2346	149	12	,	,	PUNCT
ejpam-2346	149	13	h6	h6	PROPN
ejpam-2346	149	14	,	,	PUNCT
ejpam-2346	149	15	h7	h7	PROPN
ejpam-2346	149	16	)	)	PUNCT
ejpam-2346	149	17	t	t	AUX
ejpam-2346	149	18	be	be	AUX
ejpam-2346	149	19	call	call	VERB
ejpam-2346	149	20	heptahedron	heptahedron	PROPN
ejpam-2346	149	21	where	where	SCONJ
ejpam-2346	149	22	h1	h1	PROPN
ejpam-2346	149	23	≡	≡	PROPN
ejpam-2346	149	24	(	(	PUNCT
ejpam-2346	149	25	1	1	NUM
ejpam-2346	149	26	,	,	PUNCT
ejpam-2346	149	27	0	0	NUM
ejpam-2346	149	28	,	,	PUNCT
ejpam-2346	149	29	1	1	NUM
ejpam-2346	149	30	)	)	PUNCT
ejpam-2346	149	31	,	,	PUNCT
ejpam-2346	149	32	h2	h2	PROPN
ejpam-2346	149	33	≡	≡	PROPN
ejpam-2346	149	34	(	(	PUNCT
ejpam-2346	149	35	1	1	NUM
ejpam-2346	149	36	,	,	PUNCT
ejpam-2346	149	37	5	5	NUM
ejpam-2346	149	38	,	,	PUNCT
ejpam-2346	149	39	1	1	NUM
ejpam-2346	149	40	)	)	PUNCT
ejpam-2346	149	41	,	,	PUNCT
ejpam-2346	149	42	h3	h3	NOUN
ejpam-2346	149	43	≡	≡	PROPN
ejpam-2346	149	44	(	(	PUNCT
ejpam-2346	149	45	4	4	NUM
ejpam-2346	149	46	,	,	PUNCT
ejpam-2346	149	47	1	1	NUM
ejpam-2346	149	48	,	,	PUNCT
ejpam-2346	149	49	1	1	NUM
ejpam-2346	149	50	)	)	PUNCT
ejpam-2346	149	51	,	,	PUNCT
ejpam-2346	149	52	h4	h4	PROPN
ejpam-2346	149	53	≡	≡	PROPN
ejpam-2346	149	54	(	(	PUNCT
ejpam-2346	149	55	4	4	NUM
ejpam-2346	149	56	,	,	PUNCT
ejpam-2346	149	57	6	6	NUM
ejpam-2346	149	58	,	,	PUNCT
ejpam-2346	149	59	1	1	NUM
ejpam-2346	149	60	)	)	PUNCT
ejpam-2346	149	61	,	,	PUNCT
ejpam-2346	149	62	h5	h5	PROPN
ejpam-2346	149	63	≡	≡	PROPN
ejpam-2346	149	64	(	(	PUNCT
ejpam-2346	149	65	0	0	NUM
ejpam-2346	149	66	,	,	PUNCT
ejpam-2346	149	67	3	3	NUM
ejpam-2346	149	68	,	,	PUNCT
ejpam-2346	149	69	1	1	NUM
ejpam-2346	149	70	)	)	PUNCT
ejpam-2346	149	71	,	,	PUNCT
ejpam-2346	149	72	h6	h6	PROPN
ejpam-2346	149	73	≡	≡	PROPN
ejpam-2346	149	74	(	(	PUNCT
ejpam-2346	149	75	5	5	NUM
ejpam-2346	149	76	,	,	PUNCT
ejpam-2346	149	77	3	3	NUM
ejpam-2346	149	78	,	,	PUNCT
ejpam-2346	149	79	1	1	NUM
ejpam-2346	149	80	)	)	PUNCT
ejpam-2346	149	81	,	,	PUNCT
ejpam-2346	149	82	h7	h7	PROPN
ejpam-2346	149	83	≡	≡	PROPN
ejpam-2346	149	84	(	(	PUNCT
ejpam-2346	149	85	5	5	NUM
ejpam-2346	149	86	,	,	PUNCT
ejpam-2346	149	87	0	0	NUM
ejpam-2346	149	88	,	,	PUNCT
ejpam-2346	149	89	2	2	NUM
ejpam-2346	149	90	)	)	PUNCT
ejpam-2346	149	91	and	and	CCONJ
ejpam-2346	149	92	after	after	ADP
ejpam-2346	149	93	using	use	VERB
ejpam-2346	149	94	transformation(1	transformation(1	PROPN
ejpam-2346	149	95	)	)	PUNCT
ejpam-2346	149	96	,	,	PUNCT
ejpam-2346	149	97	we	we	PRON
ejpam-2346	149	98	get	get	VERB
ejpam-2346	149	99	h′1	h′1	VERB
ejpam-2346	149	100	≡	≡	PROPN
ejpam-2346	149	101	(	(	PUNCT
ejpam-2346	149	102	1.02	1.02	NUM
ejpam-2346	149	103	,	,	PUNCT
ejpam-2346	149	104	.06	.06	NUM
ejpam-2346	149	105	,	,	PUNCT
ejpam-2346	149	106	.9	.9	NUM
ejpam-2346	149	107	)	)	PUNCT
ejpam-2346	149	108	,	,	PUNCT
ejpam-2346	149	109	h′2	h′2	PROPN
ejpam-2346	149	110	≡	≡	PROPN
ejpam-2346	149	111	(	(	PUNCT
ejpam-2346	149	112	.9	.9	NUM
ejpam-2346	149	113	,	,	PUNCT
ejpam-2346	149	114	5	5	NUM
ejpam-2346	149	115	,	,	PUNCT
ejpam-2346	149	116	1.1	1.1	NUM
ejpam-2346	149	117	)	)	PUNCT
ejpam-2346	149	118	,	,	PUNCT
ejpam-2346	149	119	h′3	h′3	NOUN
ejpam-2346	149	120	≡	≡	PROPN
ejpam-2346	149	121	(	(	PUNCT
ejpam-2346	149	122	4	4	NUM
ejpam-2346	149	123	,	,	PUNCT
ejpam-2346	149	124	.9	.9	NUM
ejpam-2346	149	125	,	,	PUNCT
ejpam-2346	149	126	.9	.9	NUM
ejpam-2346	149	127	)	)	PUNCT
ejpam-2346	149	128	,	,	PUNCT
ejpam-2346	149	129	h′4	h′4	NOUN
ejpam-2346	149	130	≡	≡	PROPN
ejpam-2346	149	131	(	(	PUNCT
ejpam-2346	149	132	.4	.4	PROPN
ejpam-2346	149	133	,	,	PUNCT
ejpam-2346	149	134	6.03	6.03	NUM
ejpam-2346	149	135	,	,	PUNCT
ejpam-2346	149	136	1.1	1.1	NUM
ejpam-2346	149	137	)	)	PUNCT
ejpam-2346	149	138	,	,	PUNCT
ejpam-2346	149	139	h′5	h′5	NOUN
ejpam-2346	149	140	≡	≡	PROPN
ejpam-2346	149	141	(	(	PUNCT
ejpam-2346	149	142	−.02	−.02	PROPN
ejpam-2346	149	143	,	,	PUNCT
ejpam-2346	149	144	3.03	3.03	NUM
ejpam-2346	149	145	,	,	PUNCT
ejpam-2346	149	146	1.1	1.1	NUM
ejpam-2346	149	147	)	)	PUNCT
ejpam-2346	149	148	,	,	PUNCT
ejpam-2346	149	149	h′6	h′6	ADJ
ejpam-2346	149	150	≡	≡	PROPN
ejpam-2346	149	151	(	(	PUNCT
ejpam-2346	149	152	5.02	5.02	NUM
ejpam-2346	149	153	,	,	PUNCT
ejpam-2346	149	154	3	3	NUM
ejpam-2346	149	155	,	,	PUNCT
ejpam-2346	149	156	.9	.9	NUM
ejpam-2346	149	157	)	)	PUNCT
ejpam-2346	149	158	,	,	PUNCT
ejpam-2346	149	159	h′7	h′7	NOUN
ejpam-2346	149	160	≡	≡	PROPN
ejpam-2346	149	161	(	(	PUNCT
ejpam-2346	149	162	5	5	NUM
ejpam-2346	149	163	,	,	PUNCT
ejpam-2346	149	164	0	0	NUM
ejpam-2346	149	165	,	,	PUNCT
ejpam-2346	149	166	2.1	2.1	NUM
ejpam-2346	149	167	)	)	PUNCT
ejpam-2346	149	168	centroid	centroid	NOUN
ejpam-2346	149	169	of	of	ADP
ejpam-2346	149	170	the	the	DET
ejpam-2346	149	171	heptahedron	heptahedron	NOUN
ejpam-2346	149	172	before	before	ADP
ejpam-2346	149	173	transformation	transformation	NOUN
ejpam-2346	149	174	(	(	PUNCT
ejpam-2346	149	175	17σ	17σ	X
ejpam-2346	149	176	7	7	NUM
ejpam-2346	149	177	i=1hi	i=1hi	VERB
ejpam-2346	149	178	)	)	PUNCT
ejpam-2346	149	179	after	after	ADP
ejpam-2346	149	180	transformation	transformation	NOUN
ejpam-2346	149	181	(	(	PUNCT
ejpam-2346	149	182	17σ	17σ	PROPN
ejpam-2346	149	183	7	7	NUM
ejpam-2346	149	184	i=1h	i=1h	NOUN
ejpam-2346	150	1	′	′	NUM
ejpam-2346	151	1	i	i	NOUN
ejpam-2346	151	2	)	)	PUNCT
ejpam-2346	151	3	(	(	PUNCT
ejpam-2346	151	4	2.8,2.6,1.1	2.8,2.6,1.1	NUM
ejpam-2346	151	5	)	)	PUNCT
ejpam-2346	151	6	(	(	PUNCT
ejpam-2346	151	7	2.8,2.5,1.1	2.8,2.5,1.1	NUM
ejpam-2346	151	8	)	)	PUNCT
ejpam-2346	151	9	hence	hence	ADV
ejpam-2346	151	10	from	from	ADP
ejpam-2346	151	11	the	the	DET
ejpam-2346	151	12	above	above	ADV
ejpam-2346	151	13	we	we	PRON
ejpam-2346	151	14	can	can	AUX
ejpam-2346	151	15	say	say	VERB
ejpam-2346	151	16	that	that	SCONJ
ejpam-2346	151	17	the	the	DET
ejpam-2346	151	18	transformation	transformation	NOUN
ejpam-2346	151	19	(	(	PUNCT
ejpam-2346	151	20	1	1	X
ejpam-2346	151	21	)	)	PUNCT
ejpam-2346	151	22	does	do	AUX
ejpam-2346	151	23	not	not	PART
ejpam-2346	151	24	preserve	preserve	VERB
ejpam-2346	151	25	the	the	DET
ejpam-2346	151	26	centroid	centroid	NOUN
ejpam-2346	151	27	of	of	ADP
ejpam-2346	151	28	the	the	DET
ejpam-2346	151	29	transformation	transformation	NOUN
ejpam-2346	151	30	,	,	PUNCT
ejpam-2346	151	31	provided	provide	VERB
ejpam-2346	151	32	after	after	ADP
ejpam-2346	151	33	transformation	transformation	NOUN
ejpam-2346	151	34	the	the	DET
ejpam-2346	151	35	base	base	NOUN
ejpam-2346	151	36	of	of	ADP
ejpam-2346	151	37	the	the	DET
ejpam-2346	151	38	heptahedron	heptahedron	NOUN
ejpam-2346	151	39	must	must	AUX
ejpam-2346	151	40	also	also	ADV
ejpam-2346	151	41	be	be	AUX
ejpam-2346	151	42	coplanar	coplanar	ADJ
ejpam-2346	151	43	.	.	PUNCT
ejpam-2346	152	1	similarly	similarly	ADV
ejpam-2346	152	2	,	,	PUNCT
ejpam-2346	152	3	we	we	PRON
ejpam-2346	152	4	can	can	AUX
ejpam-2346	152	5	also	also	ADV
ejpam-2346	152	6	show	show	VERB
ejpam-2346	152	7	that	that	SCONJ
ejpam-2346	152	8	the	the	DET
ejpam-2346	152	9	transformation	transformation	NOUN
ejpam-2346	152	10	(	(	PUNCT
ejpam-2346	152	11	2	2	X
ejpam-2346	152	12	)	)	PUNCT
ejpam-2346	152	13	does	do	AUX
ejpam-2346	152	14	not	not	PART
ejpam-2346	152	15	preserve	preserve	VERB
ejpam-2346	152	16	the	the	DET
ejpam-2346	152	17	centroid	centroid	NOUN
ejpam-2346	152	18	of	of	ADP
ejpam-2346	152	19	transformation	transformation	NOUN
ejpam-2346	152	20	by	by	ADP
ejpam-2346	152	21	the	the	DET
ejpam-2346	152	22	following	follow	VERB
ejpam-2346	152	23	table	table	NOUN
ejpam-2346	152	24	centroid	centroid	NOUN
ejpam-2346	152	25	of	of	ADP
ejpam-2346	152	26	the	the	DET
ejpam-2346	152	27	heptahedron	heptahedron	NOUN
ejpam-2346	152	28	before	before	ADP
ejpam-2346	152	29	transformation	transformation	NOUN
ejpam-2346	152	30	(	(	PUNCT
ejpam-2346	152	31	17σ	17σ	X
ejpam-2346	152	32	7	7	NUM
ejpam-2346	152	33	i=1hi	i=1hi	VERB
ejpam-2346	152	34	)	)	PUNCT
ejpam-2346	152	35	after	after	ADP
ejpam-2346	152	36	transformation	transformation	NOUN
ejpam-2346	152	37	(	(	PUNCT
ejpam-2346	152	38	17σ	17σ	PROPN
ejpam-2346	152	39	7	7	NUM
ejpam-2346	152	40	i=1h	i=1h	NOUN
ejpam-2346	153	1	′	′	NUM
ejpam-2346	154	1	i	i	NOUN
ejpam-2346	154	2	)	)	PUNCT
ejpam-2346	154	3	(	(	PUNCT
ejpam-2346	154	4	2.8,2.6,1.1	2.8,2.6,1.1	NUM
ejpam-2346	154	5	)	)	PUNCT
ejpam-2346	154	6	(	(	PUNCT
ejpam-2346	154	7	2.8,2.6,1.2	2.8,2.6,1.2	NUM
ejpam-2346	154	8	)	)	PUNCT
ejpam-2346	154	9	s.	s.	PROPN
ejpam-2346	154	10	dey	dey	PROPN
ejpam-2346	154	11	,	,	PUNCT
ejpam-2346	154	12	b.	b.	PROPN
ejpam-2346	154	13	pal	pal	PROPN
ejpam-2346	154	14	,	,	PUNCT
ejpam-2346	154	15	a.	a.	NOUN
ejpam-2346	154	16	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	154	17	/	/	SYM
ejpam-2346	154	18	eur	eur	PROPN
ejpam-2346	154	19	.	.	PUNCT
ejpam-2346	155	1	j.	j.	PROPN
ejpam-2346	155	2	pure	pure	PROPN
ejpam-2346	155	3	appl	appl	PROPN
ejpam-2346	155	4	.	.	PROPN
ejpam-2346	155	5	math	math	PROPN
ejpam-2346	155	6	,	,	PUNCT
ejpam-2346	155	7	11	11	NUM
ejpam-2346	155	8	(	(	PUNCT
ejpam-2346	155	9	1	1	NUM
ejpam-2346	155	10	)	)	PUNCT
ejpam-2346	155	11	(	(	PUNCT
ejpam-2346	155	12	2018	2018	NUM
ejpam-2346	155	13	)	)	PUNCT
ejpam-2346	155	14	,	,	PUNCT
ejpam-2346	155	15	315	315	NUM
ejpam-2346	155	16	-	-	SYM
ejpam-2346	155	17	330	330	NUM
ejpam-2346	155	18	323	323	NUM
ejpam-2346	155	19	example	example	NOUN
ejpam-2346	155	20	5	5	NUM
ejpam-2346	155	21	.	.	PUNCT
ejpam-2346	156	1	in	in	ADP
ejpam-2346	156	2	this	this	DET
ejpam-2346	156	3	example	example	NOUN
ejpam-2346	156	4	,	,	PUNCT
ejpam-2346	156	5	we	we	PRON
ejpam-2346	156	6	show	show	VERB
ejpam-2346	156	7	that	that	SCONJ
ejpam-2346	156	8	transformation	transformation	NOUN
ejpam-2346	156	9	(	(	PUNCT
ejpam-2346	156	10	3	3	X
ejpam-2346	156	11	)	)	PUNCT
ejpam-2346	156	12	does	do	AUX
ejpam-2346	156	13	not	not	PART
ejpam-2346	156	14	preserve	preserve	VERB
ejpam-2346	156	15	centroid	centroid	NOUN
ejpam-2346	156	16	of	of	ADP
ejpam-2346	156	17	transformation	transformation	NOUN
ejpam-2346	156	18	,	,	PUNCT
ejpam-2346	156	19	provided	provide	VERB
ejpam-2346	156	20	after	after	ADP
ejpam-2346	156	21	transformation	transformation	NOUN
ejpam-2346	156	22	the	the	DET
ejpam-2346	156	23	base	base	NOUN
ejpam-2346	156	24	of	of	ADP
ejpam-2346	156	25	the	the	DET
ejpam-2346	156	26	heptahedron	heptahedron	NOUN
ejpam-2346	156	27	must	must	AUX
ejpam-2346	156	28	also	also	ADV
ejpam-2346	156	29	be	be	AUX
ejpam-2346	156	30	coplanar	coplanar	ADJ
ejpam-2346	156	31	.	.	PUNCT
ejpam-2346	157	1	we	we	PRON
ejpam-2346	157	2	take	take	VERB
ejpam-2346	157	3	same	same	ADJ
ejpam-2346	157	4	co	co	NOUN
ejpam-2346	157	5	-	-	NOUN
ejpam-2346	157	6	ordinates	ordinate	NOUN
ejpam-2346	157	7	of	of	ADP
ejpam-2346	157	8	heptahedron	heptahedron	NOUN
ejpam-2346	157	9	as	as	ADP
ejpam-2346	157	10	taken	take	VERB
ejpam-2346	157	11	as	as	ADP
ejpam-2346	157	12	example	example	NOUN
ejpam-2346	157	13	(	(	PUNCT
ejpam-2346	157	14	1	1	NUM
ejpam-2346	157	15	)	)	PUNCT
ejpam-2346	157	16	,	,	PUNCT
ejpam-2346	157	17	we	we	PRON
ejpam-2346	157	18	get	get	VERB
ejpam-2346	157	19	the	the	DET
ejpam-2346	157	20	following	follow	VERB
ejpam-2346	157	21	table	table	NOUN
ejpam-2346	157	22	centroid	centroid	NOUN
ejpam-2346	157	23	of	of	ADP
ejpam-2346	157	24	the	the	DET
ejpam-2346	157	25	heptahedron	heptahedron	NOUN
ejpam-2346	157	26	before	before	ADP
ejpam-2346	157	27	transformation	transformation	NOUN
ejpam-2346	157	28	(	(	PUNCT
ejpam-2346	157	29	17σ	17σ	X
ejpam-2346	157	30	7	7	NUM
ejpam-2346	157	31	i=1hi	i=1hi	VERB
ejpam-2346	157	32	)	)	PUNCT
ejpam-2346	157	33	after	after	ADP
ejpam-2346	157	34	transformation	transformation	NOUN
ejpam-2346	157	35	(	(	PUNCT
ejpam-2346	157	36	17σ	17σ	PROPN
ejpam-2346	157	37	7	7	NUM
ejpam-2346	157	38	i=1h	i=1h	NOUN
ejpam-2346	157	39	′	′	NUM
ejpam-2346	158	1	i	i	NOUN
ejpam-2346	158	2	)	)	PUNCT
ejpam-2346	158	3	(	(	PUNCT
ejpam-2346	158	4	2.8,2.6,1.1	2.8,2.6,1.1	NUM
ejpam-2346	158	5	)	)	PUNCT
ejpam-2346	158	6	(	(	PUNCT
ejpam-2346	158	7	3.2,2.2,1.2	3.2,2.2,1.2	NOUN
ejpam-2346	158	8	)	)	PUNCT
ejpam-2346	158	9	similarly	similarly	ADV
ejpam-2346	158	10	,	,	PUNCT
ejpam-2346	158	11	we	we	PRON
ejpam-2346	158	12	can	can	AUX
ejpam-2346	158	13	also	also	ADV
ejpam-2346	158	14	show	show	VERB
ejpam-2346	158	15	that	that	SCONJ
ejpam-2346	158	16	transformation	transformation	NOUN
ejpam-2346	158	17	(	(	PUNCT
ejpam-2346	158	18	4	4	X
ejpam-2346	158	19	)	)	PUNCT
ejpam-2346	158	20	does	do	AUX
ejpam-2346	158	21	not	not	PART
ejpam-2346	158	22	preserve	preserve	VERB
ejpam-2346	158	23	the	the	DET
ejpam-2346	158	24	centroid	centroid	NOUN
ejpam-2346	158	25	of	of	ADP
ejpam-2346	158	26	transformation	transformation	NOUN
ejpam-2346	158	27	.	.	PUNCT
ejpam-2346	159	1	example	example	NOUN
ejpam-2346	160	1	6	6	NUM
ejpam-2346	160	2	.	.	PUNCT
ejpam-2346	161	1	here	here	ADV
ejpam-2346	161	2	,	,	PUNCT
ejpam-2346	161	3	we	we	PRON
ejpam-2346	161	4	show	show	VERB
ejpam-2346	161	5	that	that	SCONJ
ejpam-2346	161	6	transformation	transformation	NOUN
ejpam-2346	161	7	(	(	PUNCT
ejpam-2346	161	8	5	5	X
ejpam-2346	161	9	)	)	PUNCT
ejpam-2346	161	10	does	do	AUX
ejpam-2346	161	11	not	not	PART
ejpam-2346	161	12	satisfy	satisfy	VERB
ejpam-2346	161	13	the	the	DET
ejpam-2346	161	14	preserving	preserve	VERB
ejpam-2346	161	15	property	property	NOUN
ejpam-2346	161	16	of	of	ADP
ejpam-2346	161	17	centroid	centroid	NOUN
ejpam-2346	161	18	of	of	ADP
ejpam-2346	161	19	transformation	transformation	NOUN
ejpam-2346	161	20	.	.	PUNCT
ejpam-2346	162	1	we	we	PRON
ejpam-2346	162	2	take	take	VERB
ejpam-2346	162	3	same	same	ADJ
ejpam-2346	162	4	co	co	NOUN
ejpam-2346	162	5	-	-	NOUN
ejpam-2346	162	6	ordinates	ordinate	NOUN
ejpam-2346	162	7	of	of	ADP
ejpam-2346	162	8	heptahedron	heptahedron	NOUN
ejpam-2346	162	9	as	as	ADP
ejpam-2346	162	10	taken	take	VERB
ejpam-2346	162	11	as	as	ADP
ejpam-2346	162	12	example	example	NOUN
ejpam-2346	162	13	(	(	PUNCT
ejpam-2346	162	14	1	1	NUM
ejpam-2346	162	15	)	)	PUNCT
ejpam-2346	162	16	,	,	PUNCT
ejpam-2346	162	17	we	we	PRON
ejpam-2346	162	18	get	get	VERB
ejpam-2346	162	19	the	the	DET
ejpam-2346	162	20	following	follow	VERB
ejpam-2346	162	21	table	table	NOUN
ejpam-2346	162	22	centroid	centroid	NOUN
ejpam-2346	162	23	of	of	ADP
ejpam-2346	162	24	the	the	DET
ejpam-2346	162	25	heptahedron	heptahedron	NOUN
ejpam-2346	162	26	before	before	ADP
ejpam-2346	162	27	transformation	transformation	NOUN
ejpam-2346	162	28	(	(	PUNCT
ejpam-2346	162	29	17σ	17σ	X
ejpam-2346	162	30	7	7	NUM
ejpam-2346	162	31	i=1hi	i=1hi	VERB
ejpam-2346	162	32	)	)	PUNCT
ejpam-2346	162	33	after	after	ADP
ejpam-2346	162	34	transformation	transformation	NOUN
ejpam-2346	162	35	(	(	PUNCT
ejpam-2346	162	36	17σ	17σ	PROPN
ejpam-2346	162	37	7	7	NUM
ejpam-2346	162	38	i=1h	i=1h	NOUN
ejpam-2346	162	39	′	′	NUM
ejpam-2346	163	1	i	i	NOUN
ejpam-2346	163	2	)	)	PUNCT
ejpam-2346	163	3	(	(	PUNCT
ejpam-2346	163	4	2.8,2.6,1.1	2.8,2.6,1.1	NUM
ejpam-2346	163	5	)	)	PUNCT
ejpam-2346	163	6	(	(	PUNCT
ejpam-2346	163	7	2.5,3,1	2.5,3,1	NUM
ejpam-2346	163	8	)	)	PUNCT
ejpam-2346	163	9	4.3	4.3	NUM
ejpam-2346	163	10	characterization	characterization	NOUN
ejpam-2346	163	11	of	of	ADP
ejpam-2346	163	12	mean	mean	ADJ
ejpam-2346	163	13	ratio	ratio	NOUN
ejpam-2346	163	14	quality	quality	NOUN
ejpam-2346	163	15	of	of	ADP
ejpam-2346	163	16	a	a	DET
ejpam-2346	163	17	heptahedron	heptahedron	NOUN
ejpam-2346	163	18	:	:	PUNCT
ejpam-2346	163	19	to	to	PART
ejpam-2346	163	20	define	define	VERB
ejpam-2346	163	21	mean	mean	ADJ
ejpam-2346	163	22	ratio	ratio	NOUN
ejpam-2346	163	23	quality	quality	NOUN
ejpam-2346	163	24	for	for	ADP
ejpam-2346	163	25	heptahedron	heptahedron	NOUN
ejpam-2346	163	26	,	,	PUNCT
ejpam-2346	163	27	first	first	ADV
ejpam-2346	163	28	we	we	PRON
ejpam-2346	163	29	use	use	VERB
ejpam-2346	163	30	bdame	bdame	NOUN
ejpam-2346	163	31	to	to	PART
ejpam-2346	163	32	get	get	VERB
ejpam-2346	163	33	six	six	NUM
ejpam-2346	163	34	tetrahedra	tetrahedron	NOUN
ejpam-2346	163	35	and	and	CCONJ
ejpam-2346	163	36	then	then	ADV
ejpam-2346	163	37	choose	choose	VERB
ejpam-2346	163	38	any	any	DET
ejpam-2346	163	39	tetrahedron	tetrahedron	NOUN
ejpam-2346	163	40	.	.	PUNCT
ejpam-2346	164	1	let	let	VERB
ejpam-2346	164	2	t	t	NOUN
ejpam-2346	164	3	:	:	PUNCT
ejpam-2346	164	4	=	=	SYM
ejpam-2346	164	5	(	(	PUNCT
ejpam-2346	164	6	h1	h1	PROPN
ejpam-2346	164	7	,	,	PUNCT
ejpam-2346	164	8	h2	h2	PROPN
ejpam-2346	164	9	,	,	PUNCT
ejpam-2346	164	10	h3	h3	NOUN
ejpam-2346	164	11	,	,	PUNCT
ejpam-2346	164	12	h4	h4	PROPN
ejpam-2346	164	13	)	)	PUNCT
ejpam-2346	164	14	denote	denote	VERB
ejpam-2346	164	15	a	a	DET
ejpam-2346	164	16	tetrahedron	tetrahedron	NOUN
ejpam-2346	164	17	with	with	ADP
ejpam-2346	164	18	the	the	DET
ejpam-2346	164	19	four	four	NUM
ejpam-2346	164	20	pairwise	pairwise	NOUN
ejpam-2346	164	21	disjoint	disjoint	NOUN
ejpam-2346	164	22	nodes	nod	VERB
ejpam-2346	164	23	hi	hi	PROPN
ejpam-2346	164	24	∈	∈	PROPN
ejpam-2346	164	25	r3	r3	PROPN
ejpam-2346	164	26	,	,	PUNCT
ejpam-2346	164	27	i	i	PRON
ejpam-2346	164	28	∈	∈	PROPN
ejpam-2346	164	29	{	{	PUNCT
ejpam-2346	164	30	1	1	NUM
ejpam-2346	164	31	,	,	PUNCT
ejpam-2346	164	32	...	...	PUNCT
ejpam-2346	164	33	,	,	PUNCT
ejpam-2346	164	34	4	4	NUM
ejpam-2346	164	35	}	}	PUNCT
ejpam-2346	164	36	,	,	PUNCT
ejpam-2346	164	37	which	which	PRON
ejpam-2346	164	38	is	be	AUX
ejpam-2346	164	39	positively	positively	ADV
ejpam-2346	164	40	oriented	orient	VERB
ejpam-2346	164	41	.	.	PUNCT
ejpam-2346	165	1	that	that	PRON
ejpam-2346	165	2	is	be	AUX
ejpam-2346	165	3	det(a	det(a	PROPN
ejpam-2346	165	4	)	)	PUNCT
ejpam-2346	165	5	>	>	X
ejpam-2346	165	6	0	0	PUNCT
ejpam-2346	166	1	with	with	ADP
ejpam-2346	166	2	a	a	DET
ejpam-2346	166	3	:	:	PUNCT
ejpam-2346	166	4	=	=	SYM
ejpam-2346	166	5	(	(	PUNCT
ejpam-2346	166	6	h2	h2	PROPN
ejpam-2346	166	7	−	−	PROPN
ejpam-2346	166	8	h1	h1	PROPN
ejpam-2346	166	9	,	,	PUNCT
ejpam-2346	166	10	h3	h3	VERB
ejpam-2346	166	11	−	−	PROPN
ejpam-2346	166	12	h1	h1	PROPN
ejpam-2346	166	13	,	,	PUNCT
ejpam-2346	166	14	h4	h4	PROPN
ejpam-2346	166	15	−	−	PROPN
ejpam-2346	166	16	h1	h1	PROPN
ejpam-2346	166	17	)	)	PUNCT
ejpam-2346	166	18	representing	represent	VERB
ejpam-2346	166	19	the	the	DET
ejpam-2346	166	20	(	(	PUNCT
ejpam-2346	166	21	3×	3×	NUM
ejpam-2346	166	22	3	3	NUM
ejpam-2346	166	23	)	)	PUNCT
ejpam-2346	166	24	jacobian	jacobian	ADJ
ejpam-2346	166	25	matrix	matrix	NOUN
ejpam-2346	166	26	of	of	ADP
ejpam-2346	166	27	the	the	DET
ejpam-2346	166	28	difference	difference	NOUN
ejpam-2346	166	29	vectors	vector	NOUN
ejpam-2346	166	30	,	,	PUNCT
ejpam-2346	166	31	which	which	PRON
ejpam-2346	166	32	span	span	VERB
ejpam-2346	166	33	the	the	DET
ejpam-2346	166	34	tetrahedron	tetrahedron	NOUN
ejpam-2346	166	35	.	.	PUNCT
ejpam-2346	167	1	in	in	ADP
ejpam-2346	167	2	[	[	X
ejpam-2346	167	3	4	4	NUM
ejpam-2346	167	4	,	,	PUNCT
ejpam-2346	167	5	7	7	NUM
ejpam-2346	167	6	,	,	PUNCT
ejpam-2346	167	7	14–16	14–16	NUM
ejpam-2346	167	8	]	]	PUNCT
ejpam-2346	167	9	,	,	PUNCT
ejpam-2346	167	10	authors	author	NOUN
ejpam-2346	167	11	have	have	AUX
ejpam-2346	167	12	discussed	discuss	VERB
ejpam-2346	167	13	how	how	SCONJ
ejpam-2346	167	14	to	to	PART
ejpam-2346	167	15	get	get	VERB
ejpam-2346	167	16	mean	mean	VERB
ejpam-2346	167	17	ratio	ratio	NOUN
ejpam-2346	167	18	quality	quality	NOUN
ejpam-2346	167	19	of	of	ADP
ejpam-2346	167	20	a	a	DET
ejpam-2346	167	21	tetrahedron	tetrahedron	NOUN
ejpam-2346	167	22	and	and	CCONJ
ejpam-2346	167	23	using	use	VERB
ejpam-2346	167	24	this	this	DET
ejpam-2346	167	25	procedure	procedure	NOUN
ejpam-2346	167	26	we	we	PRON
ejpam-2346	167	27	define	define	VERB
ejpam-2346	167	28	the	the	DET
ejpam-2346	167	29	mean	mean	ADJ
ejpam-2346	167	30	ratio	ratio	NOUN
ejpam-2346	167	31	quality	quality	NOUN
ejpam-2346	167	32	for	for	ADP
ejpam-2346	167	33	heptahedron	heptahedron	NOUN
ejpam-2346	167	34	,	,	PUNCT
ejpam-2346	167	35	q(h	q(h	PROPN
ejpam-2346	167	36	)	)	PUNCT
ejpam-2346	167	37	:	:	PUNCT
ejpam-2346	168	1	=	=	SYM
ejpam-2346	168	2	1	1	NUM
ejpam-2346	168	3	6	6	NUM
ejpam-2346	168	4	6	6	NUM
ejpam-2346	168	5	∑	∑	NOUN
ejpam-2346	168	6	k=1	k=1	NOUN
ejpam-2346	168	7	3det(sk	3det(sk	NUM
ejpam-2346	168	8	)	)	PUNCT
ejpam-2346	168	9	2/3	2/3	NUM
ejpam-2346	168	10	‖s‖f	‖s‖f	NOUN
ejpam-2346	168	11	,	,	PUNCT
ejpam-2346	168	12	where	where	SCONJ
ejpam-2346	168	13	‖s‖	‖s‖	PROPN
ejpam-2346	168	14	:	:	PUNCT
ejpam-2346	168	15	=	=	PUNCT
ejpam-2346	168	16	trace	trace	NOUN
ejpam-2346	168	17	√	√	PROPN
ejpam-2346	168	18	(	(	PUNCT
ejpam-2346	168	19	sts	st	NOUN
ejpam-2346	168	20	)	)	PUNCT
ejpam-2346	168	21	denote	denote	VERB
ejpam-2346	168	22	the	the	DET
ejpam-2346	168	23	frobenious	frobenious	ADJ
ejpam-2346	168	24	norm	norm	NOUN
ejpam-2346	168	25	of	of	ADP
ejpam-2346	168	26	the	the	DET
ejpam-2346	168	27	matrix	matrix	NOUN
ejpam-2346	168	28	sk	sk	X
ejpam-2346	168	29	=	=	PUNCT
ejpam-2346	168	30	akw	akw	PROPN
ejpam-2346	168	31	−1	−1	NOUN
ejpam-2346	168	32	and	and	CCONJ
ejpam-2346	168	33	w	w	PROPN
ejpam-2346	168	34	=	=	NOUN
ejpam-2346	168	35			NOUN
ejpam-2346	168	36			NOUN
ejpam-2346	168	37	1	1	NUM
ejpam-2346	168	38	1/2	1/2	NUM
ejpam-2346	168	39	1/2	1/2	NUM
ejpam-2346	168	40	0	0	NUM
ejpam-2346	168	41	√	√	PROPN
ejpam-2346	168	42	3/2	3/2	NUM
ejpam-2346	168	43	√	√	NUM
ejpam-2346	168	44	3/6	3/6	NUM
ejpam-2346	168	45	0	0	NUM
ejpam-2346	168	46	0	0	NUM
ejpam-2346	168	47	√	√	NUM
ejpam-2346	168	48	3/	3/	NUM
ejpam-2346	168	49	√	√	NUM
ejpam-2346	168	50	2	2	NUM
ejpam-2346	168	51			NOUN
ejpam-2346	168	52			PUNCT
ejpam-2346	169	1	denotes	denote	VERB
ejpam-2346	169	2	the	the	DET
ejpam-2346	169	3	difference	difference	NOUN
ejpam-2346	169	4	matrix	matrix	NOUN
ejpam-2346	169	5	of	of	ADP
ejpam-2346	169	6	a	a	DET
ejpam-2346	169	7	regular	regular	ADJ
ejpam-2346	169	8	reference	reference	NOUN
ejpam-2346	169	9	tetrahedron	tetrahedron	NOUN
ejpam-2346	169	10	.	.	PUNCT
ejpam-2346	170	1	now	now	ADV
ejpam-2346	170	2	in	in	ADP
ejpam-2346	170	3	the	the	DET
ejpam-2346	170	4	case	case	NOUN
ejpam-2346	170	5	of	of	ADP
ejpam-2346	170	6	heptahedron	heptahedron	NOUN
ejpam-2346	170	7	,	,	PUNCT
ejpam-2346	170	8	the	the	DET
ejpam-2346	170	9	criterion	criterion	NOUN
ejpam-2346	170	10	of	of	ADP
ejpam-2346	170	11	q(h	q(h	PROPN
ejpam-2346	170	12	)	)	PUNCT
ejpam-2346	170	13	is	be	AUX
ejpam-2346	170	14	not	not	PART
ejpam-2346	170	15	same	same	ADJ
ejpam-2346	170	16	as	as	ADP
ejpam-2346	170	17	in	in	ADP
ejpam-2346	170	18	[	[	X
ejpam-2346	170	19	15	15	NUM
ejpam-2346	170	20	,	,	PUNCT
ejpam-2346	170	21	16	16	NUM
ejpam-2346	170	22	]	]	PUNCT
ejpam-2346	170	23	.	.	PUNCT
ejpam-2346	171	1	in	in	ADP
ejpam-2346	171	2	that	that	DET
ejpam-2346	171	3	case	case	NOUN
ejpam-2346	171	4	,	,	PUNCT
ejpam-2346	171	5	if	if	SCONJ
ejpam-2346	171	6	h	h	NOUN
ejpam-2346	171	7	is	be	AUX
ejpam-2346	171	8	regular	regular	ADJ
ejpam-2346	171	9	then	then	ADV
ejpam-2346	171	10	q(h	q(h	NUM
ejpam-2346	171	11	)	)	PUNCT
ejpam-2346	171	12	∈	∈	PROPN
ejpam-2346	172	1	[	[	X
ejpam-2346	172	2	0	0	NUM
ejpam-2346	172	3	,	,	PUNCT
ejpam-2346	172	4	1	1	NUM
ejpam-2346	172	5	]	]	PUNCT
ejpam-2346	172	6	,	,	PUNCT
ejpam-2346	172	7	where	where	SCONJ
ejpam-2346	172	8	very	very	ADV
ejpam-2346	172	9	small	small	ADJ
ejpam-2346	172	10	values	value	NOUN
ejpam-2346	172	11	indicate	indicate	VERB
ejpam-2346	172	12	nearly	nearly	ADV
ejpam-2346	172	13	degenerated	degenerated	ADJ
ejpam-2346	172	14	elements	element	NOUN
ejpam-2346	172	15	and	and	CCONJ
ejpam-2346	172	16	large	large	ADJ
ejpam-2346	172	17	s.	s.	PROPN
ejpam-2346	172	18	dey	dey	PROPN
ejpam-2346	172	19	,	,	PUNCT
ejpam-2346	172	20	b.	b.	PROPN
ejpam-2346	172	21	pal	pal	PROPN
ejpam-2346	172	22	,	,	PUNCT
ejpam-2346	172	23	a.	a.	NOUN
ejpam-2346	172	24	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	172	25	/	/	SYM
ejpam-2346	172	26	eur	eur	PROPN
ejpam-2346	172	27	.	.	PUNCT
ejpam-2346	173	1	j.	j.	PROPN
ejpam-2346	173	2	pure	pure	PROPN
ejpam-2346	173	3	appl	appl	PROPN
ejpam-2346	173	4	.	.	PROPN
ejpam-2346	173	5	math	math	PROPN
ejpam-2346	173	6	,	,	PUNCT
ejpam-2346	173	7	11	11	NUM
ejpam-2346	173	8	(	(	PUNCT
ejpam-2346	173	9	1	1	NUM
ejpam-2346	173	10	)	)	PUNCT
ejpam-2346	173	11	(	(	PUNCT
ejpam-2346	173	12	2018	2018	NUM
ejpam-2346	173	13	)	)	PUNCT
ejpam-2346	173	14	,	,	PUNCT
ejpam-2346	173	15	315	315	NUM
ejpam-2346	173	16	-	-	SYM
ejpam-2346	173	17	330	330	NUM
ejpam-2346	173	18	324	324	NUM
ejpam-2346	173	19	values	value	NOUN
ejpam-2346	173	20	element	element	VERB
ejpam-2346	173	21	good	good	ADJ
ejpam-2346	173	22	quality	quality	NOUN
ejpam-2346	173	23	.	.	PUNCT
ejpam-2346	174	1	now	now	ADV
ejpam-2346	174	2	,	,	PUNCT
ejpam-2346	174	3	if	if	SCONJ
ejpam-2346	174	4	the	the	DET
ejpam-2346	174	5	transformation	transformation	NOUN
ejpam-2346	174	6	is	be	AUX
ejpam-2346	174	7	applied	apply	VERB
ejpam-2346	174	8	iteratively	iteratively	ADV
ejpam-2346	174	9	,	,	PUNCT
ejpam-2346	174	10	the	the	DET
ejpam-2346	174	11	resulting	result	VERB
ejpam-2346	174	12	heptahedron	heptahedron	NOUN
ejpam-2346	174	13	became	become	VERB
ejpam-2346	174	14	more	more	ADV
ejpam-2346	174	15	and	and	CCONJ
ejpam-2346	174	16	more	more	ADV
ejpam-2346	174	17	regular	regular	ADJ
ejpam-2346	174	18	.	.	PUNCT
ejpam-2346	175	1	in	in	ADP
ejpam-2346	175	2	order	order	NOUN
ejpam-2346	175	3	to	to	PART
ejpam-2346	175	4	assess	assess	VERB
ejpam-2346	175	5	the	the	DET
ejpam-2346	175	6	regularity	regularity	NOUN
ejpam-2346	175	7	of	of	ADP
ejpam-2346	175	8	a	a	DET
ejpam-2346	175	9	heptahedron	heptahedron	ADJ
ejpam-2346	175	10	h	h	NOUN
ejpam-2346	175	11	numerically	numerically	ADV
ejpam-2346	175	12	,	,	PUNCT
ejpam-2346	175	13	the	the	DET
ejpam-2346	175	14	mean	mean	ADJ
ejpam-2346	175	15	ratio	ratio	NOUN
ejpam-2346	175	16	quality	quality	NOUN
ejpam-2346	175	17	criterion	criterion	NOUN
ejpam-2346	175	18	will	will	AUX
ejpam-2346	175	19	be	be	AUX
ejpam-2346	175	20	used	use	VERB
ejpam-2346	175	21	.	.	PUNCT
ejpam-2346	176	1	now	now	ADV
ejpam-2346	176	2	,	,	PUNCT
ejpam-2346	176	3	we	we	PRON
ejpam-2346	176	4	give	give	VERB
ejpam-2346	176	5	an	an	DET
ejpam-2346	176	6	example	example	NOUN
ejpam-2346	176	7	of	of	ADP
ejpam-2346	176	8	a	a	DET
ejpam-2346	176	9	heptahedron	heptahedron	NOUN
ejpam-2346	176	10	which	which	PRON
ejpam-2346	176	11	is	be	AUX
ejpam-2346	176	12	regular	regular	ADJ
ejpam-2346	176	13	base	base	NOUN
ejpam-2346	176	14	heptahedron	heptahedron	NOUN
ejpam-2346	176	15	but	but	CCONJ
ejpam-2346	176	16	q(h	q(h	NUM
ejpam-2346	176	17	)	)	PUNCT
ejpam-2346	176	18	6=	6=	ADP
ejpam-2346	176	19	1	1	NUM
ejpam-2346	176	20	.	.	PUNCT
ejpam-2346	176	21	example	example	NOUN
ejpam-2346	177	1	7	7	NUM
ejpam-2346	177	2	.	.	PUNCT
ejpam-2346	178	1	let	let	VERB
ejpam-2346	178	2	(	(	PUNCT
ejpam-2346	178	3	h1	h1	VERB
ejpam-2346	178	4	,	,	PUNCT
ejpam-2346	178	5	..........	..........	PUNCT
ejpam-2346	178	6	,	,	PUNCT
ejpam-2346	178	7	h7	h7	PROPN
ejpam-2346	178	8	)	)	PUNCT
ejpam-2346	178	9	t	t	PROPN
ejpam-2346	178	10	be	be	AUX
ejpam-2346	178	11	call	call	VERB
ejpam-2346	178	12	heptahedron	heptahedron	PROPN
ejpam-2346	179	1	where	where	SCONJ
ejpam-2346	179	2	h1	h1	PROPN
ejpam-2346	179	3	≡	≡	PROPN
ejpam-2346	179	4	(	(	PUNCT
ejpam-2346	179	5	5	5	NUM
ejpam-2346	179	6	,	,	PUNCT
ejpam-2346	179	7	4	4	NUM
ejpam-2346	179	8	,	,	PUNCT
ejpam-2346	179	9	5	5	NUM
ejpam-2346	179	10	)	)	PUNCT
ejpam-2346	179	11	,	,	PUNCT
ejpam-2346	179	12	h2	h2	PROPN
ejpam-2346	179	13	≡	≡	PROPN
ejpam-2346	179	14	(	(	PUNCT
ejpam-2346	179	15	5	5	NUM
ejpam-2346	179	16	,	,	PUNCT
ejpam-2346	179	17	9	9	NUM
ejpam-2346	179	18	,	,	PUNCT
ejpam-2346	179	19	5	5	NUM
ejpam-2346	179	20	)	)	PUNCT
ejpam-2346	179	21	,	,	PUNCT
ejpam-2346	179	22	h3	h3	NOUN
ejpam-2346	179	23	≡	≡	PROPN
ejpam-2346	179	24	(	(	PUNCT
ejpam-2346	179	25	0	0	NUM
ejpam-2346	179	26	,	,	PUNCT
ejpam-2346	179	27	9	9	NUM
ejpam-2346	179	28	,	,	PUNCT
ejpam-2346	179	29	5	5	NUM
ejpam-2346	179	30	)	)	PUNCT
ejpam-2346	179	31	,	,	PUNCT
ejpam-2346	179	32	h4	h4	PROPN
ejpam-2346	179	33	≡	≡	PROPN
ejpam-2346	179	34	(	(	PUNCT
ejpam-2346	179	35	0	0	NUM
ejpam-2346	179	36	,	,	PUNCT
ejpam-2346	179	37	4	4	NUM
ejpam-2346	179	38	,	,	PUNCT
ejpam-2346	179	39	5	5	NUM
ejpam-2346	179	40	)	)	PUNCT
ejpam-2346	179	41	,	,	PUNCT
ejpam-2346	179	42	h5	h5	PROPN
ejpam-2346	179	43	≡	≡	PROPN
ejpam-2346	179	44	(	(	PUNCT
ejpam-2346	179	45	3	3	NUM
ejpam-2346	179	46	,	,	PUNCT
ejpam-2346	179	47	8	8	NUM
ejpam-2346	179	48	,	,	PUNCT
ejpam-2346	179	49	5	5	NUM
ejpam-2346	179	50	)	)	PUNCT
ejpam-2346	179	51	,	,	PUNCT
ejpam-2346	179	52	h6	h6	PROPN
ejpam-2346	179	53	≡	≡	PROPN
ejpam-2346	179	54	(	(	PUNCT
ejpam-2346	179	55	8	8	NUM
ejpam-2346	179	56	,	,	PUNCT
ejpam-2346	179	57	8	8	NUM
ejpam-2346	179	58	,	,	PUNCT
ejpam-2346	179	59	5	5	NUM
ejpam-2346	179	60	)	)	PUNCT
ejpam-2346	179	61	,	,	PUNCT
ejpam-2346	179	62	h7	h7	PROPN
ejpam-2346	179	63	≡	≡	PROPN
ejpam-2346	179	64	(	(	PUNCT
ejpam-2346	179	65	4	4	NUM
ejpam-2346	179	66	,	,	PUNCT
ejpam-2346	179	67	9	9	NUM
ejpam-2346	179	68	,	,	PUNCT
ejpam-2346	179	69	11	11	NUM
ejpam-2346	179	70	)	)	PUNCT
ejpam-2346	179	71	.	.	PUNCT
ejpam-2346	180	1	here	here	ADV
ejpam-2346	180	2	,	,	PUNCT
ejpam-2346	180	3	q(h	q(h	X
ejpam-2346	180	4	)	)	PUNCT
ejpam-2346	180	5	=	=	PUNCT
ejpam-2346	181	1	0.417	0.417	NUM
ejpam-2346	181	2	.	.	PUNCT
ejpam-2346	182	1	4.4	4.4	NUM
ejpam-2346	182	2	significance	significance	NOUN
ejpam-2346	182	3	of	of	ADP
ejpam-2346	182	4	the	the	DET
ejpam-2346	182	5	scaling	scale	VERB
ejpam-2346	182	6	factor	factor	NOUN
ejpam-2346	182	7	σ	σ	PROPN
ejpam-2346	182	8	:	:	PUNCT
ejpam-2346	182	9	σ	σ	PROPN
ejpam-2346	182	10	is	be	AUX
ejpam-2346	182	11	playing	play	VERB
ejpam-2346	182	12	a	a	DET
ejpam-2346	182	13	important	important	ADJ
ejpam-2346	182	14	role	role	NOUN
ejpam-2346	182	15	to	to	PART
ejpam-2346	182	16	regularize	regularize	VERB
ejpam-2346	182	17	a	a	DET
ejpam-2346	182	18	heptahedron	heptahedron	NOUN
ejpam-2346	182	19	and	and	CCONJ
ejpam-2346	182	20	the	the	DET
ejpam-2346	182	21	speed	speed	NOUN
ejpam-2346	182	22	of	of	ADP
ejpam-2346	182	23	the	the	DET
ejpam-2346	182	24	regularization.the	regularization.the	NOUN
ejpam-2346	182	25	resulting	result	VERB
ejpam-2346	182	26	iteration	iteration	NOUN
ejpam-2346	182	27	numbers	number	NOUN
ejpam-2346	182	28	are	be	AUX
ejpam-2346	182	29	totally	totally	ADV
ejpam-2346	182	30	depended	depend	VERB
ejpam-2346	182	31	upon	upon	SCONJ
ejpam-2346	182	32	the	the	DET
ejpam-2346	182	33	scaling	scale	VERB
ejpam-2346	182	34	factor	factor	NOUN
ejpam-2346	182	35	σ	σ	PROPN
ejpam-2346	182	36	.	.	PUNCT
ejpam-2346	183	1	also	also	ADV
ejpam-2346	183	2	the	the	DET
ejpam-2346	183	3	important	important	ADJ
ejpam-2346	183	4	fact	fact	NOUN
ejpam-2346	183	5	is	be	AUX
ejpam-2346	183	6	that	that	SCONJ
ejpam-2346	183	7	there	there	PRON
ejpam-2346	183	8	is	be	VERB
ejpam-2346	183	9	no	no	DET
ejpam-2346	183	10	specific	specific	ADJ
ejpam-2346	183	11	choice	choice	NOUN
ejpam-2346	183	12	of	of	ADP
ejpam-2346	183	13	σ	σ	PROPN
ejpam-2346	183	14	,	,	PUNCT
ejpam-2346	183	15	for	for	ADP
ejpam-2346	183	16	which	which	PRON
ejpam-2346	183	17	the	the	DET
ejpam-2346	183	18	transformation	transformation	NOUN
ejpam-2346	183	19	given	give	VERB
ejpam-2346	183	20	exactly	exactly	ADV
ejpam-2346	183	21	once	once	ADV
ejpam-2346	183	22	to	to	ADP
ejpam-2346	183	23	any	any	DET
ejpam-2346	183	24	arbitrary	arbitrary	ADJ
ejpam-2346	183	25	heptahedron	heptahedron	NOUN
ejpam-2346	183	26	results	result	VERB
ejpam-2346	183	27	a	a	DET
ejpam-2346	183	28	regular	regular	ADJ
ejpam-2346	183	29	one	one	NUM
ejpam-2346	183	30	.	.	PUNCT
ejpam-2346	184	1	to	to	PART
ejpam-2346	184	2	show	show	VERB
ejpam-2346	184	3	this	this	PRON
ejpam-2346	184	4	,	,	PUNCT
ejpam-2346	184	5	we	we	PRON
ejpam-2346	184	6	give	give	VERB
ejpam-2346	184	7	an	an	DET
ejpam-2346	184	8	example	example	NOUN
ejpam-2346	184	9	.	.	PUNCT
ejpam-2346	185	1	example	example	NOUN
ejpam-2346	185	2	8	8	NUM
ejpam-2346	185	3	.	.	PUNCT
ejpam-2346	186	1	let	let	VERB
ejpam-2346	186	2	us	we	PRON
ejpam-2346	186	3	choose	choose	VERB
ejpam-2346	186	4	the	the	DET
ejpam-2346	186	5	heptahedron	heptahedron	NOUN
ejpam-2346	186	6	with	with	ADP
ejpam-2346	186	7	the	the	DET
ejpam-2346	186	8	same	same	ADJ
ejpam-2346	186	9	coordinate	coordinate	NOUN
ejpam-2346	186	10	as	as	SCONJ
ejpam-2346	186	11	given	give	VERB
ejpam-2346	186	12	in	in	ADP
ejpam-2346	186	13	article	article	NOUN
ejpam-2346	186	14	(	(	PUNCT
ejpam-2346	186	15	4.2	4.2	NUM
ejpam-2346	186	16	)	)	PUNCT
ejpam-2346	186	17	example	example	NOUN
ejpam-2346	187	1	1	1	NUM
ejpam-2346	187	2	.	.	PUNCT
ejpam-2346	187	3	according	accord	VERB
ejpam-2346	187	4	to	to	ADP
ejpam-2346	187	5	(	(	PUNCT
ejpam-2346	187	6	1	1	NUM
ejpam-2346	187	7	)	)	PUNCT
ejpam-2346	187	8	,	,	PUNCT
ejpam-2346	187	9	the	the	DET
ejpam-2346	187	10	nodes	node	NOUN
ejpam-2346	187	11	of	of	ADP
ejpam-2346	187	12	the	the	DET
ejpam-2346	187	13	transformed	transform	VERB
ejpam-2346	187	14	heptahedron	heptahedron	PROPN
ejpam-2346	187	15	h	h	NOUN
ejpam-2346	187	16	′	′	NOUN
ejpam-2346	187	17	are	be	AUX
ejpam-2346	187	18	given	give	VERB
ejpam-2346	187	19	by	by	ADP
ejpam-2346	187	20	h′1	h′1	ADJ
ejpam-2346	187	21	≡	≡	PROPN
ejpam-2346	187	22	(	(	PUNCT
ejpam-2346	187	23	1+σ(.8	1+σ(.8	NUM
ejpam-2346	187	24	)	)	PUNCT
ejpam-2346	187	25	,	,	PUNCT
ejpam-2346	187	26	0+σ(.6	0+σ(.6	NOUN
ejpam-2346	187	27	)	)	PUNCT
ejpam-2346	187	28	,	,	PUNCT
ejpam-2346	187	29	1+σ(−.2	1+σ(−.2	NUM
ejpam-2346	187	30	)	)	PUNCT
ejpam-2346	187	31	)	)	PUNCT
ejpam-2346	187	32	,	,	PUNCT
ejpam-2346	187	33	h′2	h′2	PROPN
ejpam-2346	187	34	≡	≡	PROPN
ejpam-2346	187	35	(	(	PUNCT
ejpam-2346	187	36	1+σ(−.7	1+σ(−.7	NUM
ejpam-2346	187	37	)	)	PUNCT
ejpam-2346	187	38	,	,	PUNCT
ejpam-2346	187	39	5+σ(0	5+σ(0	NUM
ejpam-2346	187	40	)	)	PUNCT
ejpam-2346	187	41	,	,	PUNCT
ejpam-2346	187	42	1+σ(.7	1+σ(.7	NUM
ejpam-2346	187	43	)	)	PUNCT
ejpam-2346	187	44	)	)	PUNCT
ejpam-2346	187	45	,	,	PUNCT
ejpam-2346	187	46	h′3	h′3	NOUN
ejpam-2346	187	47	≡	≡	PROPN
ejpam-2346	187	48	(	(	PUNCT
ejpam-2346	187	49	4+σ(.1	4+σ(.1	PROPN
ejpam-2346	187	50	)	)	PUNCT
ejpam-2346	187	51	,	,	PUNCT
ejpam-2346	187	52	1+σ(−.1	1+σ(−.1	NUM
ejpam-2346	187	53	)	)	PUNCT
ejpam-2346	187	54	,	,	PUNCT
ejpam-2346	187	55	1+σ(−.9	1+σ(−.9	NUM
ejpam-2346	187	56	)	)	PUNCT
ejpam-2346	187	57	)	)	PUNCT
ejpam-2346	187	58	,	,	PUNCT
ejpam-2346	187	59	h′4	h′4	NOUN
ejpam-2346	187	60	≡	≡	PROPN
ejpam-2346	187	61	(	(	PUNCT
ejpam-2346	187	62	4+σ(0	4+σ(0	NOUN
ejpam-2346	187	63	)	)	PUNCT
ejpam-2346	187	64	,	,	PUNCT
ejpam-2346	187	65	6+σ(.3	6+σ(.3	NUM
ejpam-2346	187	66	)	)	PUNCT
ejpam-2346	187	67	,	,	PUNCT
ejpam-2346	187	68	1+σ(.9	1+σ(.9	NUM
ejpam-2346	187	69	)	)	PUNCT
ejpam-2346	187	70	)	)	PUNCT
ejpam-2346	187	71	,	,	PUNCT
ejpam-2346	187	72	h′5	h′5	NOUN
ejpam-2346	187	73	≡	≡	PROPN
ejpam-2346	187	74	(	(	PUNCT
ejpam-2346	187	75	0+σ(−.2	0+σ(−.2	PROPN
ejpam-2346	187	76	)	)	PUNCT
ejpam-2346	187	77	,	,	PUNCT
ejpam-2346	187	78	3	3	NUM
ejpam-2346	187	79	+	+	NUM
ejpam-2346	187	80	σ(.3	σ(.3	NUM
ejpam-2346	187	81	)	)	PUNCT
ejpam-2346	187	82	,	,	PUNCT
ejpam-2346	187	83	1+σ(.9	1+σ(.9	NUM
ejpam-2346	187	84	)	)	PUNCT
ejpam-2346	187	85	)	)	PUNCT
ejpam-2346	187	86	,	,	PUNCT
ejpam-2346	187	87	h′6	h′6	ADJ
ejpam-2346	187	88	≡	≡	PROPN
ejpam-2346	187	89	(	(	PUNCT
ejpam-2346	187	90	5+σ(.2	5+σ(.2	NUM
ejpam-2346	187	91	)	)	PUNCT
ejpam-2346	187	92	,	,	PUNCT
ejpam-2346	187	93	3+σ(0	3+σ(0	NUM
ejpam-2346	187	94	)	)	PUNCT
ejpam-2346	187	95	,	,	PUNCT
ejpam-2346	187	96	1+σ(−.9	1+σ(−.9	NUM
ejpam-2346	187	97	)	)	PUNCT
ejpam-2346	187	98	)	)	PUNCT
ejpam-2346	187	99	and	and	CCONJ
ejpam-2346	187	100	h′7	h′7	X
ejpam-2346	187	101	≡	≡	PROPN
ejpam-2346	187	102	(	(	PUNCT
ejpam-2346	187	103	5+σ(0	5+σ(0	NUM
ejpam-2346	187	104	)	)	PUNCT
ejpam-2346	187	105	,	,	PUNCT
ejpam-2346	187	106	0+σ(0	0+σ(0	NUM
ejpam-2346	187	107	)	)	PUNCT
ejpam-2346	187	108	,	,	PUNCT
ejpam-2346	187	109	2+σ(1	2+σ(1	NOUN
ejpam-2346	187	110	)	)	PUNCT
ejpam-2346	187	111	)	)	PUNCT
ejpam-2346	187	112	using	use	VERB
ejpam-2346	187	113	an	an	DET
ejpam-2346	187	114	arbitrary	arbitrary	ADJ
ejpam-2346	187	115	scaling	scaling	NOUN
ejpam-2346	187	116	factor	factor	NOUN
ejpam-2346	187	117	σ	σ	PROPN
ejpam-2346	187	118	∈	∈	PROPN
ejpam-2346	187	119	r+	r+	NOUN
ejpam-2346	187	120	0	0	PUNCT
ejpam-2346	187	121	.	.	PUNCT
ejpam-2346	188	1	in	in	ADP
ejpam-2346	188	2	order	order	NOUN
ejpam-2346	188	3	to	to	PART
ejpam-2346	188	4	be	be	AUX
ejpam-2346	188	5	regular	regular	ADJ
ejpam-2346	188	6	,	,	PUNCT
ejpam-2346	188	7	all	all	DET
ejpam-2346	188	8	the	the	DET
ejpam-2346	188	9	base	base	NOUN
ejpam-2346	188	10	lengths	length	NOUN
ejpam-2346	188	11	of	of	ADP
ejpam-2346	188	12	the	the	DET
ejpam-2346	188	13	transformed	transform	VERB
ejpam-2346	188	14	heptahedron	heptahedron	NOUN
ejpam-2346	188	15	must	must	AUX
ejpam-2346	188	16	be	be	AUX
ejpam-2346	188	17	equal	equal	ADJ
ejpam-2346	188	18	.	.	PUNCT
ejpam-2346	189	1	but	but	CCONJ
ejpam-2346	189	2	,	,	PUNCT
ejpam-2346	189	3	we	we	PRON
ejpam-2346	189	4	see	see	VERB
ejpam-2346	189	5	that	that	SCONJ
ejpam-2346	189	6	|h′1	|h′1	ADJ
ejpam-2346	189	7	−	−	NOUN
ejpam-2346	189	8	h′2|	h′2|	NOUN
ejpam-2346	189	9	=	=	NOUN
ejpam-2346	189	10	|h′2	|h′2	NOUN
ejpam-2346	189	11	−	−	NOUN
ejpam-2346	189	12	h′3|	h′3|	NOUN
ejpam-2346	189	13	for	for	ADP
ejpam-2346	189	14	σ	σ	NOUN
ejpam-2346	189	15	=	=	SYM
ejpam-2346	189	16	55.2	55.2	NUM
ejpam-2346	189	17	,	,	PUNCT
ejpam-2346	189	18	|h′2	|h′2	VERB
ejpam-2346	189	19	−	−	NOUN
ejpam-2346	189	20	h′3|	h′3|	NOUN
ejpam-2346	190	1	=	=	SYM
ejpam-2346	190	2	|h′3	|h′3	NOUN
ejpam-2346	190	3	−	−	PROPN
ejpam-2346	190	4	h′4|	h′4|	NOUN
ejpam-2346	190	5	for	for	ADP
ejpam-2346	190	6	σ	σ	PROPN
ejpam-2346	190	7	=	=	SYM
ejpam-2346	190	8	8	8	NUM
ejpam-2346	190	9	,	,	PUNCT
ejpam-2346	190	10	|h′3	|h′3	NOUN
ejpam-2346	190	11	−	−	PROPN
ejpam-2346	190	12	h′4|	h′4|	NOUN
ejpam-2346	190	13	=	=	SYM
ejpam-2346	190	14	|h′4	|h′4	NOUN
ejpam-2346	190	15	−	−	PROPN
ejpam-2346	190	16	h′5|	h′5|	NOUN
ejpam-2346	190	17	for	for	ADP
ejpam-2346	190	18	σ	σ	PROPN
ejpam-2346	190	19	=	=	SYM
ejpam-2346	190	20	0.71	0.71	NUM
ejpam-2346	190	21	,	,	PUNCT
ejpam-2346	190	22	|h′4	|h′4	NOUN
ejpam-2346	190	23	−	−	NOUN
ejpam-2346	190	24	h′5|	h′5|	NOUN
ejpam-2346	190	25	=	=	NOUN
ejpam-2346	190	26	|h′5	|h′5	NOUN
ejpam-2346	190	27	−	−	PROPN
ejpam-2346	190	28	h′6|	h′6|	NOUN
ejpam-2346	190	29	for	for	ADP
ejpam-2346	190	30	σ	σ	PROPN
ejpam-2346	190	31	=	=	SYM
ejpam-2346	190	32	0.69	0.69	NUM
ejpam-2346	190	33	,	,	PUNCT
ejpam-2346	190	34	|h′5	|h′5	NOUN
ejpam-2346	190	35	−	−	PROPN
ejpam-2346	190	36	h′6|	h′6|	NOUN
ejpam-2346	190	37	=	=	NOUN
ejpam-2346	190	38	|h′6	|h′6	ADJ
ejpam-2346	190	39	−	−	NOUN
ejpam-2346	190	40	h′1|	h′1|	NOUN
ejpam-2346	190	41	for	for	ADP
ejpam-2346	190	42	σ	σ	PROPN
ejpam-2346	190	43	=	=	PROPN
ejpam-2346	190	44	5.4	5.4	NUM
ejpam-2346	190	45	.	.	PUNCT
ejpam-2346	191	1	so	so	ADV
ejpam-2346	191	2	,	,	PUNCT
ejpam-2346	191	3	we	we	PRON
ejpam-2346	191	4	see	see	VERB
ejpam-2346	191	5	that	that	SCONJ
ejpam-2346	191	6	there	there	PRON
ejpam-2346	191	7	is	be	VERB
ejpam-2346	191	8	no	no	DET
ejpam-2346	191	9	specific	specific	ADJ
ejpam-2346	191	10	σ	σ	PROPN
ejpam-2346	191	11	∈	∈	PROPN
ejpam-2346	191	12	r+	r+	NOUN
ejpam-2346	191	13	0	0	NUM
ejpam-2346	191	14	for	for	ADP
ejpam-2346	191	15	which	which	PRON
ejpam-2346	191	16	the	the	DET
ejpam-2346	191	17	heptahedron	heptahedron	PROPN
ejpam-2346	191	18	h	h	NOUN
ejpam-2346	191	19	′	′	NUM
ejpam-2346	191	20	obtained	obtain	VERB
ejpam-2346	191	21	by	by	ADP
ejpam-2346	191	22	one	one	NUM
ejpam-2346	191	23	step	step	NOUN
ejpam-2346	191	24	of	of	ADP
ejpam-2346	191	25	the	the	DET
ejpam-2346	191	26	transformation	transformation	NOUN
ejpam-2346	191	27	is	be	AUX
ejpam-2346	191	28	regular	regular	ADJ
ejpam-2346	191	29	.	.	PUNCT
ejpam-2346	192	1	4.5	4.5	NUM
ejpam-2346	192	2	uniqueness	uniqueness	NOUN
ejpam-2346	192	3	of	of	ADP
ejpam-2346	192	4	the	the	DET
ejpam-2346	192	5	circumsphere	circumsphere	NOUN
ejpam-2346	192	6	of	of	ADP
ejpam-2346	192	7	heptahedron	heptahedron	NOUN
ejpam-2346	192	8	:	:	PUNCT
ejpam-2346	192	9	now	now	ADV
ejpam-2346	192	10	for	for	ADP
ejpam-2346	192	11	any	any	DET
ejpam-2346	192	12	3	3	NUM
ejpam-2346	192	13	-	-	PUNCT
ejpam-2346	192	14	simplex	simplex	NOUN
ejpam-2346	192	15	,	,	PUNCT
ejpam-2346	192	16	we	we	PRON
ejpam-2346	192	17	can	can	AUX
ejpam-2346	192	18	always	always	ADV
ejpam-2346	192	19	draw	draw	VERB
ejpam-2346	192	20	a	a	DET
ejpam-2346	192	21	sphere	sphere	NOUN
ejpam-2346	192	22	through	through	ADP
ejpam-2346	192	23	the	the	DET
ejpam-2346	192	24	four	four	NUM
ejpam-2346	192	25	vertices	vertex	NOUN
ejpam-2346	192	26	of	of	ADP
ejpam-2346	192	27	the	the	DET
ejpam-2346	192	28	3	3	NUM
ejpam-2346	192	29	-	-	PUNCT
ejpam-2346	192	30	simplex	simplex	NOUN
ejpam-2346	192	31	,	,	PUNCT
ejpam-2346	192	32	but	but	CCONJ
ejpam-2346	192	33	for	for	ADP
ejpam-2346	192	34	heptahedron	heptahedron	NOUN
ejpam-2346	192	35	and	and	CCONJ
ejpam-2346	192	36	other	other	ADJ
ejpam-2346	192	37	3d	3d	NUM
ejpam-2346	192	38	-	-	PUNCT
ejpam-2346	192	39	figures	figure	NOUN
ejpam-2346	192	40	we	we	PRON
ejpam-2346	192	41	always	always	ADV
ejpam-2346	192	42	do	do	AUX
ejpam-2346	192	43	not	not	PART
ejpam-2346	192	44	get	get	VERB
ejpam-2346	192	45	a	a	DET
ejpam-2346	192	46	sphere	sphere	NOUN
ejpam-2346	192	47	through	through	ADP
ejpam-2346	192	48	the	the	DET
ejpam-2346	192	49	all	all	DET
ejpam-2346	192	50	vertices	vertex	NOUN
ejpam-2346	192	51	of	of	ADP
ejpam-2346	192	52	the	the	DET
ejpam-2346	192	53	3d	3d	NUM
ejpam-2346	192	54	-	-	PUNCT
ejpam-2346	192	55	figure	figure	NOUN
ejpam-2346	192	56	except	except	SCONJ
ejpam-2346	192	57	tetrahedron	tetrahedron	NOUN
ejpam-2346	192	58	.	.	PUNCT
ejpam-2346	193	1	but	but	CCONJ
ejpam-2346	193	2	if	if	SCONJ
ejpam-2346	193	3	we	we	PRON
ejpam-2346	193	4	choose	choose	VERB
ejpam-2346	193	5	a	a	DET
ejpam-2346	193	6	heptahedron	heptahedron	NOUN
ejpam-2346	193	7	so	so	SCONJ
ejpam-2346	193	8	that	that	SCONJ
ejpam-2346	193	9	its	its	PRON
ejpam-2346	193	10	all	all	DET
ejpam-2346	193	11	vertices	vertex	NOUN
ejpam-2346	193	12	satisfy	satisfy	VERB
ejpam-2346	193	13	some	some	DET
ejpam-2346	193	14	particular	particular	ADJ
ejpam-2346	193	15	sphere	sphere	NOUN
ejpam-2346	193	16	equation	equation	NOUN
ejpam-2346	193	17	and	and	CCONJ
ejpam-2346	193	18	then	then	ADV
ejpam-2346	193	19	we	we	PRON
ejpam-2346	193	20	use	use	VERB
ejpam-2346	193	21	the	the	DET
ejpam-2346	193	22	transformation	transformation	NOUN
ejpam-2346	193	23	(	(	PUNCT
ejpam-2346	193	24	1	1	NUM
ejpam-2346	193	25	)	)	PUNCT
ejpam-2346	193	26	,	,	PUNCT
ejpam-2346	193	27	(	(	PUNCT
ejpam-2346	193	28	2	2	NUM
ejpam-2346	193	29	)	)	PUNCT
ejpam-2346	193	30	,	,	PUNCT
ejpam-2346	193	31	(	(	PUNCT
ejpam-2346	193	32	3	3	NUM
ejpam-2346	193	33	)	)	PUNCT
ejpam-2346	193	34	,	,	PUNCT
ejpam-2346	193	35	(	(	PUNCT
ejpam-2346	193	36	4	4	NUM
ejpam-2346	193	37	)	)	PUNCT
ejpam-2346	193	38	and	and	CCONJ
ejpam-2346	193	39	(	(	PUNCT
ejpam-2346	193	40	5	5	NUM
ejpam-2346	193	41	)	)	PUNCT
ejpam-2346	193	42	,	,	PUNCT
ejpam-2346	193	43	we	we	PRON
ejpam-2346	193	44	can	can	AUX
ejpam-2346	193	45	show	show	VERB
ejpam-2346	193	46	that	that	SCONJ
ejpam-2346	193	47	after	after	ADP
ejpam-2346	193	48	transformation	transformation	NOUN
ejpam-2346	193	49	the	the	DET
ejpam-2346	193	50	transformed	transform	VERB
ejpam-2346	193	51	heptahedron	heptahedron	NOUN
ejpam-2346	193	52	may	may	AUX
ejpam-2346	193	53	not	not	PART
ejpam-2346	193	54	satisfy	satisfy	VERB
ejpam-2346	193	55	some	some	DET
ejpam-2346	193	56	particular	particular	ADJ
ejpam-2346	193	57	sphere	sphere	NOUN
ejpam-2346	193	58	equation	equation	NOUN
ejpam-2346	193	59	.	.	PUNCT
ejpam-2346	194	1	let	let	VERB
ejpam-2346	194	2	us	we	PRON
ejpam-2346	194	3	give	give	VERB
ejpam-2346	194	4	an	an	DET
ejpam-2346	194	5	example	example	NOUN
ejpam-2346	194	6	using	use	VERB
ejpam-2346	194	7	transformation	transformation	NOUN
ejpam-2346	194	8	(	(	PUNCT
ejpam-2346	194	9	2	2	NUM
ejpam-2346	194	10	)	)	PUNCT
ejpam-2346	194	11	and	and	CCONJ
ejpam-2346	194	12	(	(	PUNCT
ejpam-2346	194	13	4	4	NUM
ejpam-2346	194	14	)	)	PUNCT
ejpam-2346	194	15	.	.	PUNCT
ejpam-2346	195	1	example	example	NOUN
ejpam-2346	196	1	9	9	NUM
ejpam-2346	196	2	.	.	PUNCT
ejpam-2346	197	1	let	let	VERB
ejpam-2346	197	2	h	h	NOUN
ejpam-2346	197	3	:	:	PUNCT
ejpam-2346	197	4	=	=	SYM
ejpam-2346	197	5	(	(	PUNCT
ejpam-2346	197	6	h1	h1	PROPN
ejpam-2346	197	7	,	,	PUNCT
ejpam-2346	197	8	h2	h2	PROPN
ejpam-2346	197	9	,	,	PUNCT
ejpam-2346	197	10	h3	h3	NOUN
ejpam-2346	197	11	,	,	PUNCT
ejpam-2346	197	12	h4	h4	NOUN
ejpam-2346	197	13	,	,	PUNCT
ejpam-2346	197	14	h5	h5	PROPN
ejpam-2346	197	15	,	,	PUNCT
ejpam-2346	197	16	h6	h6	PROPN
ejpam-2346	197	17	,	,	PUNCT
ejpam-2346	197	18	h7	h7	PROPN
ejpam-2346	197	19	)	)	PUNCT
ejpam-2346	197	20	t	t	PROPN
ejpam-2346	197	21	denote	denote	VERB
ejpam-2346	197	22	the	the	DET
ejpam-2346	197	23	heptahedron	heptahedron	NOUN
ejpam-2346	197	24	with	with	ADP
ejpam-2346	197	25	h1	h1	PROPN
ejpam-2346	197	26	≡	≡	PROPN
ejpam-2346	197	27	(	(	PUNCT
ejpam-2346	197	28	−.64	−.64	PROPN
ejpam-2346	197	29	,	,	PUNCT
ejpam-2346	197	30	.48	.48	NUM
ejpam-2346	197	31	,	,	PUNCT
ejpam-2346	197	32	.6	.6	NUM
ejpam-2346	197	33	)	)	PUNCT
ejpam-2346	197	34	,	,	PUNCT
ejpam-2346	197	35	h2	h2	PROPN
ejpam-2346	197	36	≡	≡	PROPN
ejpam-2346	197	37	(	(	PUNCT
ejpam-2346	197	38	.8	.8	PROPN
ejpam-2346	197	39	,	,	PUNCT
ejpam-2346	197	40	0	0	NUM
ejpam-2346	197	41	,	,	PUNCT
ejpam-2346	197	42	.6	.6	NUM
ejpam-2346	197	43	)	)	PUNCT
ejpam-2346	197	44	,	,	PUNCT
ejpam-2346	197	45	h3	h3	NOUN
ejpam-2346	197	46	≡	≡	PROPN
ejpam-2346	197	47	(	(	PUNCT
ejpam-2346	197	48	0,−.8	0,−.8	PROPN
ejpam-2346	197	49	,	,	PUNCT
ejpam-2346	197	50	.6	.6	NUM
ejpam-2346	197	51	)	)	PUNCT
ejpam-2346	197	52	,	,	PUNCT
ejpam-2346	197	53	h4	h4	PROPN
ejpam-2346	197	54	≡	≡	PROPN
ejpam-2346	197	55	(	(	PUNCT
ejpam-2346	197	56	−.8	−.8	PROPN
ejpam-2346	197	57	,	,	PUNCT
ejpam-2346	197	58	0	0	NUM
ejpam-2346	197	59	,	,	PUNCT
ejpam-2346	197	60	.6	.6	NUM
ejpam-2346	197	61	)	)	PUNCT
ejpam-2346	197	62	,	,	PUNCT
ejpam-2346	197	63	h5	h5	PROPN
ejpam-2346	197	64	≡	≡	PROPN
ejpam-2346	197	65	(	(	PUNCT
ejpam-2346	197	66	0	0	NUM
ejpam-2346	197	67	,	,	PUNCT
ejpam-2346	197	68	.8	.8	NUM
ejpam-2346	197	69	,	,	PUNCT
ejpam-2346	197	70	.6	.6	NUM
ejpam-2346	197	71	)	)	PUNCT
ejpam-2346	197	72	,	,	PUNCT
ejpam-2346	197	73	h6	h6	PROPN
ejpam-2346	197	74	≡	≡	PROPN
ejpam-2346	197	75	(	(	PUNCT
ejpam-2346	197	76	.64,−.48	.64,−.48	PROPN
ejpam-2346	197	77	,	,	PUNCT
ejpam-2346	197	78	.6	.6	NUM
ejpam-2346	197	79	)	)	PUNCT
ejpam-2346	197	80	,	,	PUNCT
ejpam-2346	197	81	h7	h7	PROPN
ejpam-2346	197	82	≡	≡	PROPN
ejpam-2346	197	83	(	(	PUNCT
ejpam-2346	197	84	0	0	NUM
ejpam-2346	197	85	,	,	PUNCT
ejpam-2346	197	86	0	0	NUM
ejpam-2346	197	87	,	,	PUNCT
ejpam-2346	197	88	1	1	NUM
ejpam-2346	197	89	)	)	PUNCT
ejpam-2346	197	90	.	.	PUNCT
ejpam-2346	198	1	we	we	PRON
ejpam-2346	198	2	see	see	VERB
ejpam-2346	198	3	that	that	SCONJ
ejpam-2346	198	4	all	all	DET
ejpam-2346	198	5	these	these	DET
ejpam-2346	198	6	points	point	NOUN
ejpam-2346	198	7	are	be	AUX
ejpam-2346	198	8	satisfy	satisfy	VERB
ejpam-2346	198	9	the	the	DET
ejpam-2346	198	10	sphere	sphere	NOUN
ejpam-2346	198	11	equation	equation	NOUN
ejpam-2346	198	12	s.	s.	PROPN
ejpam-2346	198	13	dey	dey	PROPN
ejpam-2346	198	14	,	,	PUNCT
ejpam-2346	198	15	b.	b.	PROPN
ejpam-2346	198	16	pal	pal	PROPN
ejpam-2346	198	17	,	,	PUNCT
ejpam-2346	198	18	a.	a.	NOUN
ejpam-2346	198	19	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	198	20	/	/	SYM
ejpam-2346	198	21	eur	eur	PROPN
ejpam-2346	198	22	.	.	PUNCT
ejpam-2346	199	1	j.	j.	PROPN
ejpam-2346	199	2	pure	pure	PROPN
ejpam-2346	199	3	appl	appl	PROPN
ejpam-2346	199	4	.	.	PROPN
ejpam-2346	199	5	math	math	PROPN
ejpam-2346	199	6	,	,	PUNCT
ejpam-2346	199	7	11	11	NUM
ejpam-2346	199	8	(	(	PUNCT
ejpam-2346	199	9	1	1	NUM
ejpam-2346	199	10	)	)	PUNCT
ejpam-2346	199	11	(	(	PUNCT
ejpam-2346	199	12	2018	2018	NUM
ejpam-2346	199	13	)	)	PUNCT
ejpam-2346	199	14	,	,	PUNCT
ejpam-2346	199	15	315	315	NUM
ejpam-2346	199	16	-	-	SYM
ejpam-2346	199	17	330	330	NUM
ejpam-2346	199	18	325	325	NUM
ejpam-2346	199	19	x2	x2	NOUN
ejpam-2346	200	1	+	+	CCONJ
ejpam-2346	200	2	y2	y2	PROPN
ejpam-2346	201	1	+	+	CCONJ
ejpam-2346	201	2	z2	z2	NOUN
ejpam-2346	201	3	=	=	SYM
ejpam-2346	201	4	1	1	NUM
ejpam-2346	201	5	.	.	PUNCT
ejpam-2346	202	1	but	but	CCONJ
ejpam-2346	202	2	after	after	ADP
ejpam-2346	202	3	transformation	transformation	NOUN
ejpam-2346	202	4	using	use	VERB
ejpam-2346	202	5	(	(	PUNCT
ejpam-2346	202	6	1	1	NUM
ejpam-2346	202	7	)	)	PUNCT
ejpam-2346	202	8	,	,	PUNCT
ejpam-2346	202	9	we	we	PRON
ejpam-2346	202	10	see	see	VERB
ejpam-2346	202	11	that	that	SCONJ
ejpam-2346	202	12	they	they	PRON
ejpam-2346	202	13	do	do	AUX
ejpam-2346	202	14	not	not	PART
ejpam-2346	202	15	satisfy	satisfy	VERB
ejpam-2346	202	16	the	the	DET
ejpam-2346	202	17	sphere	sphere	NOUN
ejpam-2346	202	18	equation	equation	NOUN
ejpam-2346	202	19	.	.	PUNCT
ejpam-2346	203	1	if	if	SCONJ
ejpam-2346	203	2	we	we	PRON
ejpam-2346	203	3	use	use	VERB
ejpam-2346	203	4	transformation	transformation	NOUN
ejpam-2346	203	5	(	(	PUNCT
ejpam-2346	203	6	2	2	NUM
ejpam-2346	203	7	)	)	PUNCT
ejpam-2346	203	8	,	,	PUNCT
ejpam-2346	203	9	we	we	PRON
ejpam-2346	203	10	get	get	VERB
ejpam-2346	203	11	,	,	PUNCT
ejpam-2346	203	12	h′1	h′1	PROPN
ejpam-2346	203	13	≡	≡	PROPN
ejpam-2346	203	14	(	(	PUNCT
ejpam-2346	203	15	−.64	−.64	PROPN
ejpam-2346	203	16	,	,	PUNCT
ejpam-2346	203	17	.48	.48	NUM
ejpam-2346	203	18	,	,	PUNCT
ejpam-2346	203	19	.6	.6	NUM
ejpam-2346	203	20	)	)	PUNCT
ejpam-2346	203	21	,	,	PUNCT
ejpam-2346	203	22	h′2	h′2	PROPN
ejpam-2346	203	23	≡	≡	PROPN
ejpam-2346	203	24	(	(	PUNCT
ejpam-2346	203	25	.8	.8	PROPN
ejpam-2346	203	26	,	,	PUNCT
ejpam-2346	203	27	0	0	NUM
ejpam-2346	203	28	,	,	PUNCT
ejpam-2346	203	29	.6	.6	NUM
ejpam-2346	203	30	)	)	PUNCT
ejpam-2346	203	31	,	,	PUNCT
ejpam-2346	203	32	h′3	h′3	NOUN
ejpam-2346	203	33	≡	≡	PROPN
ejpam-2346	203	34	(	(	PUNCT
ejpam-2346	203	35	0,−.8	0,−.8	PROPN
ejpam-2346	203	36	,	,	PUNCT
ejpam-2346	203	37	.6	.6	NUM
ejpam-2346	203	38	)	)	PUNCT
ejpam-2346	203	39	,	,	PUNCT
ejpam-2346	203	40	h′4	h′4	NOUN
ejpam-2346	203	41	≡	≡	PROPN
ejpam-2346	203	42	(	(	PUNCT
ejpam-2346	203	43	−.8	−.8	PROPN
ejpam-2346	203	44	,	,	PUNCT
ejpam-2346	203	45	0	0	NUM
ejpam-2346	203	46	,	,	PUNCT
ejpam-2346	203	47	.6	.6	NUM
ejpam-2346	203	48	)	)	PUNCT
ejpam-2346	203	49	,	,	PUNCT
ejpam-2346	203	50	h′5	h′5	NOUN
ejpam-2346	203	51	≡	≡	PROPN
ejpam-2346	203	52	(	(	PUNCT
ejpam-2346	203	53	0	0	NUM
ejpam-2346	203	54	,	,	PUNCT
ejpam-2346	203	55	.8	.8	NUM
ejpam-2346	203	56	,	,	PUNCT
ejpam-2346	203	57	.6	.6	NUM
ejpam-2346	203	58	)	)	PUNCT
ejpam-2346	203	59	,	,	PUNCT
ejpam-2346	203	60	h′6	h′6	ADJ
ejpam-2346	203	61	≡	≡	PROPN
ejpam-2346	203	62	(	(	PUNCT
ejpam-2346	203	63	.64,−.48	.64,−.48	PROPN
ejpam-2346	203	64	,	,	PUNCT
ejpam-2346	203	65	.6	.6	NUM
ejpam-2346	203	66	)	)	PUNCT
ejpam-2346	203	67	,	,	PUNCT
ejpam-2346	203	68	h′7	h′7	NOUN
ejpam-2346	203	69	≡	≡	PROPN
ejpam-2346	203	70	(	(	PUNCT
ejpam-2346	203	71	0	0	NUM
ejpam-2346	203	72	,	,	PUNCT
ejpam-2346	203	73	0	0	NUM
ejpam-2346	203	74	,	,	PUNCT
ejpam-2346	203	75	1.1	1.1	NUM
ejpam-2346	203	76	)	)	PUNCT
ejpam-2346	203	77	.	.	PUNCT
ejpam-2346	204	1	we	we	PRON
ejpam-2346	204	2	see	see	VERB
ejpam-2346	204	3	that	that	SCONJ
ejpam-2346	204	4	they	they	PRON
ejpam-2346	204	5	also	also	ADV
ejpam-2346	204	6	do	do	AUX
ejpam-2346	204	7	not	not	PART
ejpam-2346	204	8	satisfy	satisfy	VERB
ejpam-2346	204	9	the	the	DET
ejpam-2346	204	10	sphere	sphere	NOUN
ejpam-2346	204	11	equation	equation	NOUN
ejpam-2346	204	12	.	.	PUNCT
ejpam-2346	205	1	one	one	PRON
ejpam-2346	205	2	can	can	AUX
ejpam-2346	205	3	show	show	VERB
ejpam-2346	205	4	that	that	SCONJ
ejpam-2346	205	5	transformation	transformation	NOUN
ejpam-2346	205	6	(	(	PUNCT
ejpam-2346	205	7	3	3	X
ejpam-2346	205	8	)	)	PUNCT
ejpam-2346	205	9	does	do	AUX
ejpam-2346	205	10	not	not	PART
ejpam-2346	205	11	satisfy	satisfy	VERB
ejpam-2346	205	12	the	the	DET
ejpam-2346	205	13	sphere	sphere	NOUN
ejpam-2346	205	14	equation	equation	NOUN
ejpam-2346	205	15	.	.	PUNCT
ejpam-2346	206	1	if	if	SCONJ
ejpam-2346	206	2	we	we	PRON
ejpam-2346	206	3	use	use	VERB
ejpam-2346	206	4	apex	apex	NOUN
ejpam-2346	206	5	transformation	transformation	NOUN
ejpam-2346	206	6	(	(	PUNCT
ejpam-2346	206	7	4	4	NUM
ejpam-2346	206	8	)	)	PUNCT
ejpam-2346	206	9	,	,	PUNCT
ejpam-2346	206	10	we	we	PRON
ejpam-2346	206	11	get	get	VERB
ejpam-2346	206	12	the	the	DET
ejpam-2346	206	13	co	co	NOUN
ejpam-2346	206	14	-	-	NOUN
ejpam-2346	206	15	ordinates	ordinate	NOUN
ejpam-2346	206	16	h′1	h′1	PROPN
ejpam-2346	206	17	≡	≡	PROPN
ejpam-2346	206	18	(	(	PUNCT
ejpam-2346	206	19	.26,−.26	.26,−.26	PROPN
ejpam-2346	206	20	,	,	PUNCT
ejpam-2346	206	21	.73	.73	NUM
ejpam-2346	206	22	)	)	PUNCT
ejpam-2346	206	23	,	,	PUNCT
ejpam-2346	206	24	h′2	h′2	PROPN
ejpam-2346	206	25	≡	≡	PROPN
ejpam-2346	206	26	(	(	PUNCT
ejpam-2346	206	27	−.26,−.26	−.26,−.26	PROPN
ejpam-2346	206	28	,	,	PUNCT
ejpam-2346	206	29	.73	.73	NUM
ejpam-2346	206	30	)	)	PUNCT
ejpam-2346	206	31	,	,	PUNCT
ejpam-2346	206	32	h′3	h′3	PROPN
ejpam-2346	206	33	≡	≡	PROPN
ejpam-2346	206	34	(	(	PUNCT
ejpam-2346	206	35	−.26	−.26	PROPN
ejpam-2346	206	36	,	,	PUNCT
ejpam-2346	206	37	.26	.26	NUM
ejpam-2346	206	38	,	,	PUNCT
ejpam-2346	206	39	.73	.73	NUM
ejpam-2346	206	40	)	)	PUNCT
ejpam-2346	206	41	,	,	PUNCT
ejpam-2346	206	42	h′4	h′4	NOUN
ejpam-2346	206	43	≡	≡	PROPN
ejpam-2346	206	44	(	(	PUNCT
ejpam-2346	206	45	.21	.21	NUM
ejpam-2346	206	46	,	,	PUNCT
ejpam-2346	206	47	.11	.11	NUM
ejpam-2346	206	48	,	,	PUNCT
ejpam-2346	206	49	.73	.73	NUM
ejpam-2346	206	50	)	)	PUNCT
ejpam-2346	206	51	,	,	PUNCT
ejpam-2346	206	52	h′5	h′5	NOUN
ejpam-2346	206	53	≡	≡	PROPN
ejpam-2346	206	54	(	(	PUNCT
ejpam-2346	206	55	0	0	NUM
ejpam-2346	206	56	,	,	PUNCT
ejpam-2346	206	57	0	0	NUM
ejpam-2346	206	58	,	,	PUNCT
ejpam-2346	206	59	.73	.73	NUM
ejpam-2346	206	60	)	)	PUNCT
ejpam-2346	206	61	,	,	PUNCT
ejpam-2346	206	62	h′6	h′6	ADJ
ejpam-2346	206	63	≡	≡	PROPN
ejpam-2346	206	64	(	(	PUNCT
ejpam-2346	206	65	.05	.05	NUM
ejpam-2346	206	66	,	,	PUNCT
ejpam-2346	206	67	.16	.16	NUM
ejpam-2346	206	68	,	,	PUNCT
ejpam-2346	206	69	.73	.73	NUM
ejpam-2346	206	70	)	)	PUNCT
ejpam-2346	206	71	,	,	PUNCT
ejpam-2346	206	72	h′7	h′7	NOUN
ejpam-2346	206	73	≡	≡	PROPN
ejpam-2346	206	74	(	(	PUNCT
ejpam-2346	206	75	0	0	NUM
ejpam-2346	206	76	,	,	PUNCT
ejpam-2346	206	77	0	0	NUM
ejpam-2346	206	78	,	,	PUNCT
ejpam-2346	206	79	.73	.73	NUM
ejpam-2346	206	80	)	)	PUNCT
ejpam-2346	206	81	we	we	PRON
ejpam-2346	206	82	see	see	VERB
ejpam-2346	206	83	that	that	SCONJ
ejpam-2346	206	84	they	they	PRON
ejpam-2346	206	85	also	also	ADV
ejpam-2346	206	86	do	do	AUX
ejpam-2346	206	87	not	not	PART
ejpam-2346	206	88	satisfy	satisfy	VERB
ejpam-2346	206	89	the	the	DET
ejpam-2346	206	90	sphere	sphere	NOUN
ejpam-2346	206	91	equation	equation	NOUN
ejpam-2346	206	92	.	.	PUNCT
ejpam-2346	207	1	example	example	NOUN
ejpam-2346	208	1	10	10	NUM
ejpam-2346	208	2	.	.	PUNCT
ejpam-2346	209	1	if	if	SCONJ
ejpam-2346	209	2	we	we	PRON
ejpam-2346	209	3	see	see	VERB
ejpam-2346	209	4	transformation	transformation	NOUN
ejpam-2346	209	5	(	(	PUNCT
ejpam-2346	209	6	5	5	NUM
ejpam-2346	209	7	)	)	PUNCT
ejpam-2346	209	8	,	,	PUNCT
ejpam-2346	209	9	the	the	DET
ejpam-2346	209	10	transformed	transform	VERB
ejpam-2346	209	11	heptahedron	heptahedron	NOUN
ejpam-2346	209	12	becomes	become	VERB
ejpam-2346	209	13	h1	h1	PROPN
ejpam-2346	209	14	≡	≡	PROPN
ejpam-2346	209	15	(	(	PUNCT
ejpam-2346	209	16	−.64	−.64	PROPN
ejpam-2346	209	17	,	,	PUNCT
ejpam-2346	209	18	.48	.48	NUM
ejpam-2346	209	19	,	,	PUNCT
ejpam-2346	209	20	.6	.6	NUM
ejpam-2346	209	21	)	)	PUNCT
ejpam-2346	209	22	,	,	PUNCT
ejpam-2346	209	23	h2	h2	PROPN
ejpam-2346	209	24	≡	≡	PROPN
ejpam-2346	209	25	(	(	PUNCT
ejpam-2346	209	26	.8	.8	PROPN
ejpam-2346	209	27	,	,	PUNCT
ejpam-2346	209	28	0	0	NUM
ejpam-2346	209	29	,	,	PUNCT
ejpam-2346	209	30	.6	.6	NUM
ejpam-2346	209	31	)	)	PUNCT
ejpam-2346	209	32	,	,	PUNCT
ejpam-2346	209	33	h3	h3	NOUN
ejpam-2346	209	34	≡	≡	PROPN
ejpam-2346	209	35	(	(	PUNCT
ejpam-2346	209	36	0,−.8	0,−.8	PROPN
ejpam-2346	209	37	,	,	PUNCT
ejpam-2346	209	38	.6	.6	NUM
ejpam-2346	209	39	)	)	PUNCT
ejpam-2346	209	40	,	,	PUNCT
ejpam-2346	209	41	h4	h4	PROPN
ejpam-2346	209	42	≡	≡	PROPN
ejpam-2346	209	43	(	(	PUNCT
ejpam-2346	209	44	−.8	−.8	PROPN
ejpam-2346	209	45	,	,	PUNCT
ejpam-2346	209	46	0	0	NUM
ejpam-2346	209	47	,	,	PUNCT
ejpam-2346	209	48	.6	.6	NUM
ejpam-2346	209	49	)	)	PUNCT
ejpam-2346	209	50	,	,	PUNCT
ejpam-2346	209	51	h5	h5	PROPN
ejpam-2346	209	52	≡	≡	PROPN
ejpam-2346	209	53	(	(	PUNCT
ejpam-2346	209	54	0	0	NUM
ejpam-2346	209	55	,	,	PUNCT
ejpam-2346	209	56	.8	.8	NUM
ejpam-2346	209	57	,	,	PUNCT
ejpam-2346	209	58	.6	.6	NUM
ejpam-2346	209	59	)	)	PUNCT
ejpam-2346	209	60	,	,	PUNCT
ejpam-2346	209	61	h6	h6	PROPN
ejpam-2346	209	62	≡	≡	PROPN
ejpam-2346	209	63	(	(	PUNCT
ejpam-2346	209	64	.64,−.48	.64,−.48	PROPN
ejpam-2346	209	65	,	,	PUNCT
ejpam-2346	209	66	.6	.6	NUM
ejpam-2346	209	67	)	)	PUNCT
ejpam-2346	209	68	,	,	PUNCT
ejpam-2346	209	69	h′7	h′7	NOUN
ejpam-2346	209	70	≡	≡	PROPN
ejpam-2346	209	71	(	(	PUNCT
ejpam-2346	209	72	0	0	NUM
ejpam-2346	209	73	,	,	PUNCT
ejpam-2346	209	74	0	0	NUM
ejpam-2346	209	75	,	,	PUNCT
ejpam-2346	209	76	1.7	1.7	NUM
ejpam-2346	209	77	)	)	PUNCT
ejpam-2346	209	78	.	.	PUNCT
ejpam-2346	210	1	we	we	PRON
ejpam-2346	210	2	see	see	VERB
ejpam-2346	210	3	that	that	SCONJ
ejpam-2346	210	4	all	all	PRON
ejpam-2346	210	5	h′i	h′i	PRON
ejpam-2346	210	6	do	do	AUX
ejpam-2346	210	7	not	not	PART
ejpam-2346	210	8	satisfy	satisfy	VERB
ejpam-2346	210	9	the	the	DET
ejpam-2346	210	10	sphere	sphere	NOUN
ejpam-2346	210	11	equation	equation	NOUN
ejpam-2346	210	12	.	.	PUNCT
ejpam-2346	211	1	5	5	X
ejpam-2346	211	2	.	.	X
ejpam-2346	211	3	regularization	regularization	NOUN
ejpam-2346	211	4	of	of	ADP
ejpam-2346	211	5	a	a	DET
ejpam-2346	211	6	heptahedron	heptahedron	NOUN
ejpam-2346	211	7	here	here	ADV
ejpam-2346	211	8	we	we	PRON
ejpam-2346	211	9	shall	shall	AUX
ejpam-2346	211	10	consider	consider	VERB
ejpam-2346	211	11	a	a	DET
ejpam-2346	211	12	process	process	NOUN
ejpam-2346	211	13	to	to	PART
ejpam-2346	211	14	regularize	regularize	VERB
ejpam-2346	211	15	a	a	DET
ejpam-2346	211	16	heptahedron	heptahedron	NOUN
ejpam-2346	211	17	.	.	PUNCT
ejpam-2346	212	1	in	in	ADP
ejpam-2346	212	2	the	the	DET
ejpam-2346	212	3	case	case	NOUN
ejpam-2346	212	4	of	of	ADP
ejpam-2346	212	5	heptahedron	heptahedron	PROPN
ejpam-2346	212	6	regular	regular	ADJ
ejpam-2346	212	7	means	mean	VERB
ejpam-2346	212	8	that	that	SCONJ
ejpam-2346	212	9	the	the	DET
ejpam-2346	212	10	base	base	NOUN
ejpam-2346	212	11	of	of	ADP
ejpam-2346	212	12	the	the	DET
ejpam-2346	212	13	heptahedron	heptahedron	NOUN
ejpam-2346	212	14	is	be	AUX
ejpam-2346	212	15	regular	regular	ADJ
ejpam-2346	212	16	and	and	CCONJ
ejpam-2346	212	17	the	the	DET
ejpam-2346	212	18	upper	upper	ADJ
ejpam-2346	212	19	all	all	DET
ejpam-2346	212	20	edge	edge	NOUN
ejpam-2346	212	21	lengths	length	NOUN
ejpam-2346	212	22	are	be	AUX
ejpam-2346	212	23	equal	equal	ADJ
ejpam-2346	212	24	.	.	PUNCT
ejpam-2346	213	1	so	so	ADV
ejpam-2346	213	2	,	,	PUNCT
ejpam-2346	213	3	when	when	SCONJ
ejpam-2346	213	4	we	we	PRON
ejpam-2346	213	5	consider	consider	VERB
ejpam-2346	213	6	an	an	DET
ejpam-2346	213	7	arbitrary	arbitrary	ADJ
ejpam-2346	213	8	heptahedron	heptahedron	NOUN
ejpam-2346	213	9	it	it	PRON
ejpam-2346	213	10	is	be	AUX
ejpam-2346	213	11	quite	quite	ADV
ejpam-2346	213	12	difficult	difficult	ADJ
ejpam-2346	213	13	to	to	PART
ejpam-2346	213	14	regularize	regularize	VERB
ejpam-2346	213	15	the	the	DET
ejpam-2346	213	16	heptahedron	heptahedron	NOUN
ejpam-2346	213	17	.	.	PUNCT
ejpam-2346	214	1	observation	observation	NOUN
ejpam-2346	214	2	5.1	5.1	NUM
ejpam-2346	214	3	if	if	SCONJ
ejpam-2346	214	4	the	the	DET
ejpam-2346	214	5	base	base	NOUN
ejpam-2346	214	6	of	of	ADP
ejpam-2346	214	7	the	the	DET
ejpam-2346	214	8	heptahedron	heptahedron	NOUN
ejpam-2346	214	9	is	be	AUX
ejpam-2346	214	10	regular	regular	ADJ
ejpam-2346	214	11	and	and	CCONJ
ejpam-2346	214	12	upper	upper	ADJ
ejpam-2346	214	13	portion	portion	NOUN
ejpam-2346	214	14	of	of	ADP
ejpam-2346	214	15	the	the	DET
ejpam-2346	214	16	heptahedron	heptahedron	NOUN
ejpam-2346	214	17	is	be	AUX
ejpam-2346	214	18	irregular	irregular	ADJ
ejpam-2346	214	19	then	then	ADV
ejpam-2346	214	20	we	we	PRON
ejpam-2346	214	21	can	can	AUX
ejpam-2346	214	22	regularize	regularize	VERB
ejpam-2346	214	23	the	the	DET
ejpam-2346	214	24	heptahedron	heptahedron	NOUN
ejpam-2346	214	25	using	use	VERB
ejpam-2346	214	26	any	any	PRON
ejpam-2346	214	27	of	of	ADP
ejpam-2346	214	28	the	the	DET
ejpam-2346	214	29	transformations	transformation	NOUN
ejpam-2346	214	30	(	(	PUNCT
ejpam-2346	214	31	1	1	NUM
ejpam-2346	214	32	)	)	PUNCT
ejpam-2346	214	33	,	,	PUNCT
ejpam-2346	214	34	(	(	PUNCT
ejpam-2346	214	35	2	2	NUM
ejpam-2346	214	36	)	)	PUNCT
ejpam-2346	214	37	,	,	PUNCT
ejpam-2346	214	38	(	(	PUNCT
ejpam-2346	214	39	3	3	NUM
ejpam-2346	214	40	)	)	PUNCT
ejpam-2346	214	41	,	,	PUNCT
ejpam-2346	214	42	(	(	PUNCT
ejpam-2346	214	43	4	4	NUM
ejpam-2346	214	44	)	)	PUNCT
ejpam-2346	214	45	and	and	CCONJ
ejpam-2346	214	46	(	(	PUNCT
ejpam-2346	214	47	5	5	NUM
ejpam-2346	214	48	)	)	PUNCT
ejpam-2346	214	49	.	.	PUNCT
ejpam-2346	215	1	this	this	PRON
ejpam-2346	215	2	can	can	AUX
ejpam-2346	215	3	be	be	AUX
ejpam-2346	215	4	verified	verify	VERB
ejpam-2346	215	5	by	by	ADP
ejpam-2346	215	6	some	some	DET
ejpam-2346	215	7	examples	example	NOUN
ejpam-2346	215	8	where	where	SCONJ
ejpam-2346	215	9	transformations	transformation	NOUN
ejpam-2346	215	10	(	(	PUNCT
ejpam-2346	215	11	2	2	NUM
ejpam-2346	215	12	)	)	PUNCT
ejpam-2346	215	13	,	,	PUNCT
ejpam-2346	215	14	(	(	PUNCT
ejpam-2346	215	15	4	4	NUM
ejpam-2346	215	16	)	)	PUNCT
ejpam-2346	215	17	and	and	CCONJ
ejpam-2346	215	18	(	(	PUNCT
ejpam-2346	215	19	5	5	X
ejpam-2346	215	20	)	)	PUNCT
ejpam-2346	215	21	are	be	AUX
ejpam-2346	215	22	used	use	VERB
ejpam-2346	215	23	to	to	PART
ejpam-2346	215	24	regularize	regularize	VERB
ejpam-2346	215	25	the	the	DET
ejpam-2346	215	26	heptahedron	heptahedron	NOUN
ejpam-2346	215	27	whose	whose	DET
ejpam-2346	215	28	base	base	NOUN
ejpam-2346	215	29	is	be	AUX
ejpam-2346	215	30	regular	regular	ADJ
ejpam-2346	215	31	.	.	PUNCT
ejpam-2346	216	1	example	example	NOUN
ejpam-2346	217	1	11	11	NUM
ejpam-2346	217	2	.	.	PUNCT
ejpam-2346	218	1	let	let	VERB
ejpam-2346	218	2	h	h	NOUN
ejpam-2346	218	3	:	:	PUNCT
ejpam-2346	218	4	=	=	SYM
ejpam-2346	218	5	(	(	PUNCT
ejpam-2346	218	6	h1	h1	PROPN
ejpam-2346	218	7	,	,	PUNCT
ejpam-2346	218	8	h2	h2	PROPN
ejpam-2346	218	9	,	,	PUNCT
ejpam-2346	218	10	h3	h3	NOUN
ejpam-2346	218	11	,	,	PUNCT
ejpam-2346	218	12	h4	h4	NOUN
ejpam-2346	218	13	,	,	PUNCT
ejpam-2346	218	14	h5	h5	PROPN
ejpam-2346	218	15	,	,	PUNCT
ejpam-2346	218	16	h6	h6	PROPN
ejpam-2346	218	17	,	,	PUNCT
ejpam-2346	218	18	h7	h7	PROPN
ejpam-2346	218	19	)	)	PUNCT
ejpam-2346	218	20	t	t	PROPN
ejpam-2346	218	21	denote	denote	VERB
ejpam-2346	218	22	a	a	DET
ejpam-2346	218	23	heptahedron	heptahedron	NOUN
ejpam-2346	218	24	with	with	ADP
ejpam-2346	218	25	h1	h1	PROPN
ejpam-2346	218	26	≡	≡	PROPN
ejpam-2346	218	27	(	(	PUNCT
ejpam-2346	218	28	5	5	NUM
ejpam-2346	218	29	,	,	PUNCT
ejpam-2346	218	30	4	4	NUM
ejpam-2346	218	31	,	,	PUNCT
ejpam-2346	218	32	5	5	NUM
ejpam-2346	218	33	)	)	PUNCT
ejpam-2346	218	34	,	,	PUNCT
ejpam-2346	218	35	h2	h2	PROPN
ejpam-2346	218	36	≡	≡	PROPN
ejpam-2346	218	37	(	(	PUNCT
ejpam-2346	218	38	5	5	NUM
ejpam-2346	218	39	,	,	PUNCT
ejpam-2346	218	40	8	8	NUM
ejpam-2346	218	41	,	,	PUNCT
ejpam-2346	218	42	5	5	NUM
ejpam-2346	218	43	)	)	PUNCT
ejpam-2346	218	44	,	,	PUNCT
ejpam-2346	218	45	h3	h3	NOUN
ejpam-2346	218	46	≡	≡	PROPN
ejpam-2346	218	47	(	(	PUNCT
ejpam-2346	218	48	1	1	NUM
ejpam-2346	218	49	,	,	PUNCT
ejpam-2346	218	50	8	8	NUM
ejpam-2346	218	51	,	,	PUNCT
ejpam-2346	218	52	5	5	NUM
ejpam-2346	218	53	)	)	PUNCT
ejpam-2346	218	54	,	,	PUNCT
ejpam-2346	218	55	h4	h4	PROPN
ejpam-2346	218	56	≡	≡	PROPN
ejpam-2346	218	57	(	(	PUNCT
ejpam-2346	218	58	1	1	NUM
ejpam-2346	218	59	,	,	PUNCT
ejpam-2346	218	60	4	4	NUM
ejpam-2346	218	61	,	,	PUNCT
ejpam-2346	218	62	5	5	NUM
ejpam-2346	218	63	)	)	PUNCT
ejpam-2346	218	64	,	,	PUNCT
ejpam-2346	218	65	h5	h5	PROPN
ejpam-2346	218	66	≡	≡	PROPN
ejpam-2346	218	67	(	(	PUNCT
ejpam-2346	218	68	1	1	NUM
ejpam-2346	218	69	,	,	PUNCT
ejpam-2346	218	70	0	0	NUM
ejpam-2346	218	71	,	,	PUNCT
ejpam-2346	218	72	5	5	NUM
ejpam-2346	218	73	)	)	PUNCT
ejpam-2346	218	74	,	,	PUNCT
ejpam-2346	218	75	h6	h6	PROPN
ejpam-2346	218	76	≡	≡	PROPN
ejpam-2346	218	77	(	(	PUNCT
ejpam-2346	218	78	5	5	NUM
ejpam-2346	218	79	,	,	PUNCT
ejpam-2346	218	80	0	0	NUM
ejpam-2346	218	81	,	,	PUNCT
ejpam-2346	218	82	5	5	NUM
ejpam-2346	218	83	)	)	PUNCT
ejpam-2346	218	84	and	and	CCONJ
ejpam-2346	218	85	h7	h7	PROPN
ejpam-2346	218	86	≡	≡	PROPN
ejpam-2346	218	87	(	(	PUNCT
ejpam-2346	218	88	4	4	NUM
ejpam-2346	218	89	,	,	PUNCT
ejpam-2346	218	90	8	8	NUM
ejpam-2346	218	91	,	,	PUNCT
ejpam-2346	218	92	10	10	NUM
ejpam-2346	218	93	)	)	PUNCT
ejpam-2346	218	94	.	.	PUNCT
ejpam-2346	219	1	this	this	DET
ejpam-2346	219	2	heptahedron	heptahedron	NOUN
ejpam-2346	219	3	is	be	AUX
ejpam-2346	219	4	not	not	PART
ejpam-2346	219	5	regular	regular	ADJ
ejpam-2346	219	6	because	because	SCONJ
ejpam-2346	219	7	the	the	DET
ejpam-2346	219	8	base	base	NOUN
ejpam-2346	219	9	edges	edge	VERB
ejpam-2346	219	10	length	length	NOUN
ejpam-2346	220	1	h1h2	h1h2	NOUN
ejpam-2346	220	2	=	=	SYM
ejpam-2346	220	3	h2h3	h2h3	NOUN
ejpam-2346	221	1	=	=	NOUN
ejpam-2346	221	2	h3h4	h3h4	NOUN
ejpam-2346	221	3	=	=	PUNCT
ejpam-2346	221	4	h4h5	h4h5	NOUN
ejpam-2346	221	5	=	=	SYM
ejpam-2346	221	6	h5h6	h5h6	X
ejpam-2346	221	7	=	=	PUNCT
ejpam-2346	221	8	h6h1	h6h1	PROPN
ejpam-2346	221	9	=	=	SYM
ejpam-2346	221	10	4	4	NUM
ejpam-2346	221	11	and	and	CCONJ
ejpam-2346	221	12	for	for	ADP
ejpam-2346	221	13	the	the	DET
ejpam-2346	221	14	upper	upper	ADJ
ejpam-2346	221	15	portion	portion	NOUN
ejpam-2346	221	16	length	length	NOUN
ejpam-2346	221	17	of	of	ADP
ejpam-2346	221	18	the	the	DET
ejpam-2346	221	19	edges	edge	NOUN
ejpam-2346	221	20	are	be	AUX
ejpam-2346	221	21	h1h7	h1h7	NOUN
ejpam-2346	221	22	=	=	VERB
ejpam-2346	221	23	6.48	6.48	NUM
ejpam-2346	221	24	,	,	PUNCT
ejpam-2346	221	25	h2h7	h2h7	X
ejpam-2346	221	26	=	=	SYM
ejpam-2346	221	27	5.09	5.09	NUM
ejpam-2346	221	28	,	,	PUNCT
ejpam-2346	221	29	h3h7	h3h7	NOUN
ejpam-2346	221	30	=	=	NOUN
ejpam-2346	221	31	5.83	5.83	NUM
ejpam-2346	221	32	,	,	PUNCT
ejpam-2346	221	33	h4h7	h4h7	NOUN
ejpam-2346	221	34	=	=	NOUN
ejpam-2346	221	35	7.07	7.07	NUM
ejpam-2346	221	36	,	,	PUNCT
ejpam-2346	221	37	h5h7	h5h7	X
ejpam-2346	221	38	=	=	SYM
ejpam-2346	221	39	9.89	9.89	NUM
ejpam-2346	221	40	,	,	PUNCT
ejpam-2346	221	41	h6h7	h6h7	NOUN
ejpam-2346	221	42	=	=	SYM
ejpam-2346	221	43	9.48	9.48	NUM
ejpam-2346	221	44	which	which	PRON
ejpam-2346	221	45	all	all	PRON
ejpam-2346	221	46	are	be	AUX
ejpam-2346	221	47	not	not	PART
ejpam-2346	221	48	equal	equal	ADJ
ejpam-2346	221	49	.	.	PUNCT
ejpam-2346	222	1	now	now	ADV
ejpam-2346	222	2	,	,	PUNCT
ejpam-2346	222	3	if	if	SCONJ
ejpam-2346	222	4	we	we	PRON
ejpam-2346	222	5	use	use	VERB
ejpam-2346	222	6	the	the	DET
ejpam-2346	222	7	transformation	transformation	NOUN
ejpam-2346	222	8	(	(	PUNCT
ejpam-2346	222	9	2	2	NUM
ejpam-2346	222	10	)	)	PUNCT
ejpam-2346	222	11	on	on	ADP
ejpam-2346	222	12	the	the	DET
ejpam-2346	222	13	given	give	VERB
ejpam-2346	222	14	heptahedron	heptahedron	NOUN
ejpam-2346	222	15	,	,	PUNCT
ejpam-2346	222	16	then	then	ADV
ejpam-2346	222	17	in	in	ADP
ejpam-2346	222	18	first	first	ADJ
ejpam-2346	222	19	step	step	NOUN
ejpam-2346	222	20	,	,	PUNCT
ejpam-2346	222	21	length	length	NOUN
ejpam-2346	222	22	of	of	ADP
ejpam-2346	222	23	the	the	DET
ejpam-2346	222	24	edges	edge	NOUN
ejpam-2346	222	25	(	(	PUNCT
ejpam-2346	222	26	upper	upper	ADJ
ejpam-2346	222	27	portion	portion	NOUN
ejpam-2346	222	28	)	)	PUNCT
ejpam-2346	222	29	are	be	AUX
ejpam-2346	222	30	h′1h	h′1h	PROPN
ejpam-2346	222	31	′	′	NUM
ejpam-2346	222	32	7	7	NUM
ejpam-2346	222	33	=	=	SYM
ejpam-2346	222	34	6.40	6.40	NUM
ejpam-2346	222	35	,	,	PUNCT
ejpam-2346	222	36	h′2h	h′2h	PROPN
ejpam-2346	222	37	′	′	NUM
ejpam-2346	222	38	7	7	NUM
ejpam-2346	222	39	=	=	SYM
ejpam-2346	222	40	5	5	NUM
ejpam-2346	222	41	,	,	PUNCT
ejpam-2346	222	42	h′3h	h′3h	PROPN
ejpam-2346	222	43	′	′	NUM
ejpam-2346	222	44	7	7	NUM
ejpam-2346	222	45	=	=	SYM
ejpam-2346	222	46	5.74	5.74	NUM
ejpam-2346	222	47	,	,	PUNCT
ejpam-2346	222	48	h′4h	h′4h	NUM
ejpam-2346	222	49	′	′	NOUN
ejpam-2346	222	50	7	7	NUM
ejpam-2346	222	51	=	=	SYM
ejpam-2346	222	52	7	7	NUM
ejpam-2346	222	53	,	,	PUNCT
ejpam-2346	222	54	h′5h	h′5h	PROPN
ejpam-2346	223	1	′	′	NOUN
ejpam-2346	223	2	7	7	NUM
ejpam-2346	223	3	=	=	SYM
ejpam-2346	223	4	9.84	9.84	NUM
ejpam-2346	223	5	,	,	PUNCT
ejpam-2346	223	6	h′6h	h′6h	PROPN
ejpam-2346	223	7	′	′	NOUN
ejpam-2346	223	8	7	7	NUM
ejpam-2346	223	9	=	=	SYM
ejpam-2346	223	10	9.43	9.43	NUM
ejpam-2346	223	11	and	and	CCONJ
ejpam-2346	223	12	in	in	ADP
ejpam-2346	223	13	2nd	2nd	ADJ
ejpam-2346	223	14	step	step	NOUN
ejpam-2346	223	15	,	,	PUNCT
ejpam-2346	223	16	length	length	NOUN
ejpam-2346	223	17	of	of	ADP
ejpam-2346	223	18	the	the	DET
ejpam-2346	223	19	edges	edge	NOUN
ejpam-2346	223	20	are	be	AUX
ejpam-2346	223	21	h′′1h	h′′1h	PRON
ejpam-2346	223	22	′′	′′	PROPN
ejpam-2346	223	23	7	7	NUM
ejpam-2346	223	24	=	=	SYM
ejpam-2346	223	25	6.32	6.32	NUM
ejpam-2346	223	26	,	,	PUNCT
ejpam-2346	223	27	h′′2h	h′′2h	X
ejpam-2346	224	1	′′	′′	PROPN
ejpam-2346	224	2	7	7	NUM
ejpam-2346	224	3	=	=	SYM
ejpam-2346	224	4	4.9	4.9	NUM
ejpam-2346	224	5	,	,	PUNCT
ejpam-2346	224	6	h′′3h	h′′3h	PROPN
ejpam-2346	224	7	′′	′′	PROPN
ejpam-2346	224	8	7	7	NUM
ejpam-2346	224	9	=	=	SYM
ejpam-2346	224	10	5.66	5.66	NUM
ejpam-2346	224	11	,	,	PUNCT
ejpam-2346	224	12	h′′4h	h′′4h	VERB
ejpam-2346	224	13	′′	′′	PROPN
ejpam-2346	224	14	7	7	NUM
ejpam-2346	224	15	=	=	SYM
ejpam-2346	224	16	6.93	6.93	NUM
ejpam-2346	224	17	,	,	PUNCT
ejpam-2346	224	18	h′′5h	h′′5h	PROPN
ejpam-2346	224	19	′′	′′	PROPN
ejpam-2346	224	20	7	7	NUM
ejpam-2346	224	21	=	=	SYM
ejpam-2346	224	22	9.80	9.80	NUM
ejpam-2346	224	23	,	,	PUNCT
ejpam-2346	224	24	h′′6h	h′′6h	DET
ejpam-2346	224	25	′′	′′	PROPN
ejpam-2346	224	26	7	7	NUM
ejpam-2346	224	27	=	=	SYM
ejpam-2346	224	28	9.38	9.38	NUM
ejpam-2346	224	29	.	.	PUNCT
ejpam-2346	225	1	here	here	ADV
ejpam-2346	225	2	we	we	PRON
ejpam-2346	225	3	observe	observe	VERB
ejpam-2346	225	4	that	that	SCONJ
ejpam-2346	225	5	the	the	DET
ejpam-2346	225	6	heptahedron	heptahedron	NOUN
ejpam-2346	225	7	tends	tend	VERB
ejpam-2346	225	8	to	to	PART
ejpam-2346	225	9	regularize	regularize	VERB
ejpam-2346	225	10	but	but	CCONJ
ejpam-2346	225	11	slowly	slowly	ADV
ejpam-2346	225	12	.	.	PUNCT
ejpam-2346	226	1	the	the	DET
ejpam-2346	226	2	speed	speed	NOUN
ejpam-2346	226	3	of	of	ADP
ejpam-2346	226	4	the	the	DET
ejpam-2346	226	5	regularization	regularization	NOUN
ejpam-2346	226	6	depends	depend	VERB
ejpam-2346	226	7	upon	upon	SCONJ
ejpam-2346	226	8	the	the	DET
ejpam-2346	226	9	choice	choice	NOUN
ejpam-2346	226	10	of	of	ADP
ejpam-2346	226	11	the	the	DET
ejpam-2346	226	12	scaling	scale	VERB
ejpam-2346	226	13	factor	factor	NOUN
ejpam-2346	226	14	σ	σ	PROPN
ejpam-2346	226	15	.	.	PUNCT
ejpam-2346	227	1	in	in	ADP
ejpam-2346	227	2	this	this	DET
ejpam-2346	227	3	case	case	NOUN
ejpam-2346	227	4	we	we	PRON
ejpam-2346	227	5	take	take	VERB
ejpam-2346	227	6	the	the	DET
ejpam-2346	227	7	scaling	scale	VERB
ejpam-2346	227	8	factor	factor	NOUN
ejpam-2346	227	9	σ	σ	NOUN
ejpam-2346	227	10	=	=	SYM
ejpam-2346	227	11	0.1	0.1	NUM
ejpam-2346	227	12	.	.	PUNCT
ejpam-2346	228	1	if	if	SCONJ
ejpam-2346	228	2	we	we	PRON
ejpam-2346	228	3	use	use	VERB
ejpam-2346	228	4	same	same	ADJ
ejpam-2346	228	5	points	point	NOUN
ejpam-2346	228	6	on	on	ADP
ejpam-2346	228	7	the	the	DET
ejpam-2346	228	8	heptahedron	heptahedron	NOUN
ejpam-2346	228	9	using	use	VERB
ejpam-2346	228	10	transformation	transformation	NOUN
ejpam-2346	228	11	(	(	PUNCT
ejpam-2346	228	12	3	3	NUM
ejpam-2346	228	13	)	)	PUNCT
ejpam-2346	228	14	,	,	PUNCT
ejpam-2346	228	15	we	we	PRON
ejpam-2346	228	16	get	get	VERB
ejpam-2346	228	17	the	the	DET
ejpam-2346	228	18	length	length	NOUN
ejpam-2346	228	19	of	of	ADP
ejpam-2346	228	20	the	the	DET
ejpam-2346	228	21	edges	edge	NOUN
ejpam-2346	228	22	(	(	PUNCT
ejpam-2346	228	23	upper	upper	ADJ
ejpam-2346	228	24	portion	portion	NOUN
ejpam-2346	228	25	)	)	PUNCT
ejpam-2346	228	26	are	be	AUX
ejpam-2346	228	27	h′1h	h′1h	PROPN
ejpam-2346	228	28	′	′	NUM
ejpam-2346	228	29	7	7	NUM
ejpam-2346	228	30	=	=	SYM
ejpam-2346	228	31	4.3	4.3	NUM
ejpam-2346	228	32	,	,	PUNCT
ejpam-2346	228	33	h′2h	h′2h	PROPN
ejpam-2346	228	34	′	′	NUM
ejpam-2346	228	35	7	7	NUM
ejpam-2346	228	36	=	=	SYM
ejpam-2346	228	37	3.3	3.3	NUM
ejpam-2346	228	38	,	,	PUNCT
ejpam-2346	228	39	h′3h	h′3h	PROPN
ejpam-2346	228	40	′	′	NUM
ejpam-2346	228	41	7	7	NUM
ejpam-2346	228	42	=	=	SYM
ejpam-2346	228	43	1.9	1.9	NUM
ejpam-2346	228	44	,	,	PUNCT
ejpam-2346	228	45	h′4h	h′4h	NUM
ejpam-2346	228	46	′	′	NOUN
ejpam-2346	228	47	7	7	NUM
ejpam-2346	228	48	=	=	SYM
ejpam-2346	228	49	2.2	2.2	NUM
ejpam-2346	228	50	,	,	PUNCT
ejpam-2346	228	51	h′5h	h′5h	PROPN
ejpam-2346	228	52	′	′	NOUN
ejpam-2346	228	53	7	7	NUM
ejpam-2346	228	54	=	=	SYM
ejpam-2346	228	55	2.5	2.5	NUM
ejpam-2346	228	56	,	,	PUNCT
ejpam-2346	228	57	h′6h	h′6h	PROPN
ejpam-2346	228	58	′	′	NOUN
ejpam-2346	228	59	7	7	NUM
ejpam-2346	228	60	=	=	SYM
ejpam-2346	228	61	3.1	3.1	NUM
ejpam-2346	228	62	.	.	PUNCT
ejpam-2346	229	1	so	so	ADV
ejpam-2346	229	2	,	,	PUNCT
ejpam-2346	229	3	we	we	PRON
ejpam-2346	229	4	see	see	VERB
ejpam-2346	229	5	that	that	SCONJ
ejpam-2346	229	6	upper	upper	ADJ
ejpam-2346	229	7	portion	portion	NOUN
ejpam-2346	229	8	of	of	ADP
ejpam-2346	229	9	this	this	DET
ejpam-2346	229	10	polyhedron	polyhedron	NOUN
ejpam-2346	229	11	is	be	AUX
ejpam-2346	229	12	not	not	PART
ejpam-2346	229	13	regular	regular	ADJ
ejpam-2346	229	14	.	.	PUNCT
ejpam-2346	230	1	but	but	CCONJ
ejpam-2346	230	2	,	,	PUNCT
ejpam-2346	230	3	we	we	PRON
ejpam-2346	230	4	look	look	VERB
ejpam-2346	230	5	after	after	ADP
ejpam-2346	230	6	transformation	transformation	NOUN
ejpam-2346	230	7	,	,	PUNCT
ejpam-2346	230	8	the	the	DET
ejpam-2346	230	9	base	base	NOUN
ejpam-2346	230	10	points	point	NOUN
ejpam-2346	230	11	are	be	AUX
ejpam-2346	230	12	regular	regular	ADJ
ejpam-2346	230	13	i.e	i.e	PRON
ejpam-2346	230	14	,	,	PUNCT
ejpam-2346	230	15	h′1h	h′1h	PROPN
ejpam-2346	230	16	′	′	NOUN
ejpam-2346	231	1	2	2	NUM
ejpam-2346	231	2	=	=	SYM
ejpam-2346	231	3	h′2h	h′2h	PROPN
ejpam-2346	231	4	′	′	NUM
ejpam-2346	231	5	3	3	NUM
ejpam-2346	231	6	=	=	SYM
ejpam-2346	231	7	h′3h	h′3h	PROPN
ejpam-2346	231	8	′	′	NOUN
ejpam-2346	231	9	4	4	NUM
ejpam-2346	231	10	=	=	NOUN
ejpam-2346	231	11	h′4h	h′4h	NOUN
ejpam-2346	231	12	′	′	NOUN
ejpam-2346	231	13	5	5	NUM
ejpam-2346	231	14	=	=	SYM
ejpam-2346	231	15	s.	s.	PROPN
ejpam-2346	231	16	dey	dey	PROPN
ejpam-2346	231	17	,	,	PUNCT
ejpam-2346	231	18	b.	b.	PROPN
ejpam-2346	231	19	pal	pal	PROPN
ejpam-2346	231	20	,	,	PUNCT
ejpam-2346	231	21	a.	a.	NOUN
ejpam-2346	231	22	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	231	23	/	/	SYM
ejpam-2346	231	24	eur	eur	PROPN
ejpam-2346	231	25	.	.	PUNCT
ejpam-2346	232	1	j.	j.	PROPN
ejpam-2346	232	2	pure	pure	PROPN
ejpam-2346	232	3	appl	appl	PROPN
ejpam-2346	232	4	.	.	PROPN
ejpam-2346	232	5	math	math	PROPN
ejpam-2346	232	6	,	,	PUNCT
ejpam-2346	232	7	11	11	NUM
ejpam-2346	232	8	(	(	PUNCT
ejpam-2346	232	9	1	1	NUM
ejpam-2346	232	10	)	)	PUNCT
ejpam-2346	232	11	(	(	PUNCT
ejpam-2346	232	12	2018	2018	NUM
ejpam-2346	232	13	)	)	PUNCT
ejpam-2346	232	14	,	,	PUNCT
ejpam-2346	232	15	315	315	NUM
ejpam-2346	232	16	-	-	SYM
ejpam-2346	232	17	330	330	NUM
ejpam-2346	232	18	326	326	NUM
ejpam-2346	232	19	h′5h	h′5h	PROPN
ejpam-2346	233	1	′	′	NOUN
ejpam-2346	233	2	6	6	NUM
ejpam-2346	233	3	=	=	SYM
ejpam-2346	233	4	h′6h	h′6h	NUM
ejpam-2346	233	5	′	′	NOUN
ejpam-2346	233	6	1	1	NUM
ejpam-2346	233	7	.	.	PUNCT
ejpam-2346	234	1	but	but	CCONJ
ejpam-2346	234	2	,	,	PUNCT
ejpam-2346	234	3	if	if	SCONJ
ejpam-2346	234	4	we	we	PRON
ejpam-2346	234	5	use	use	VERB
ejpam-2346	234	6	the	the	DET
ejpam-2346	234	7	transformation	transformation	NOUN
ejpam-2346	234	8	(	(	PUNCT
ejpam-2346	234	9	5	5	NUM
ejpam-2346	234	10	)	)	PUNCT
ejpam-2346	234	11	after	after	ADP
ejpam-2346	234	12	the	the	DET
ejpam-2346	234	13	1st	1st	ADJ
ejpam-2346	234	14	step	step	NOUN
ejpam-2346	234	15	of	of	ADP
ejpam-2346	234	16	transformation	transformation	NOUN
ejpam-2346	234	17	(	(	PUNCT
ejpam-2346	234	18	3	3	NUM
ejpam-2346	234	19	)	)	PUNCT
ejpam-2346	234	20	on	on	ADP
ejpam-2346	234	21	heptahedron	heptahedron	NOUN
ejpam-2346	234	22	,	,	PUNCT
ejpam-2346	234	23	we	we	PRON
ejpam-2346	234	24	get	get	VERB
ejpam-2346	234	25	,	,	PUNCT
ejpam-2346	234	26	h′′1	h′′1	X
ejpam-2346	235	1	=	=	SYM
ejpam-2346	235	2	h′1	h′1	ADJ
ejpam-2346	235	3	,	,	PUNCT
ejpam-2346	235	4	h	h	NOUN
ejpam-2346	235	5	′′	′′	NOUN
ejpam-2346	235	6	2	2	NUM
ejpam-2346	235	7	=	=	SYM
ejpam-2346	235	8	h′2	h′2	NOUN
ejpam-2346	235	9	,	,	PUNCT
ejpam-2346	235	10	h	h	NOUN
ejpam-2346	236	1	′′	′′	NOUN
ejpam-2346	236	2	3	3	NUM
ejpam-2346	236	3	=	=	SYM
ejpam-2346	236	4	h′3	h′3	NOUN
ejpam-2346	236	5	,	,	PUNCT
ejpam-2346	236	6	h	h	NOUN
ejpam-2346	237	1	′′	′′	NOUN
ejpam-2346	237	2	4	4	NUM
ejpam-2346	237	3	=	=	SYM
ejpam-2346	237	4	h′4	h′4	NOUN
ejpam-2346	237	5	,	,	PUNCT
ejpam-2346	237	6	h	h	NOUN
ejpam-2346	238	1	′′	′′	NOUN
ejpam-2346	238	2	5	5	NUM
ejpam-2346	238	3	=	=	SYM
ejpam-2346	238	4	h′5	h′5	NOUN
ejpam-2346	238	5	,	,	PUNCT
ejpam-2346	238	6	h	h	NOUN
ejpam-2346	239	1	′′	′′	NOUN
ejpam-2346	239	2	6	6	NUM
ejpam-2346	239	3	=	=	SYM
ejpam-2346	239	4	h′6	h′6	NOUN
ejpam-2346	239	5	and	and	CCONJ
ejpam-2346	239	6	h′′7	h′′7	NOUN
ejpam-2346	239	7	=	=	SYM
ejpam-2346	239	8	(	(	PUNCT
ejpam-2346	239	9	3.45	3.45	NUM
ejpam-2346	239	10	,	,	PUNCT
ejpam-2346	239	11	5.3	5.3	NUM
ejpam-2346	239	12	,	,	PUNCT
ejpam-2346	239	13	6.5	6.5	NUM
ejpam-2346	239	14	)	)	PUNCT
ejpam-2346	239	15	and	and	CCONJ
ejpam-2346	239	16	we	we	PRON
ejpam-2346	239	17	also	also	ADV
ejpam-2346	239	18	see	see	VERB
ejpam-2346	239	19	that	that	SCONJ
ejpam-2346	239	20	the	the	DET
ejpam-2346	239	21	length	length	NOUN
ejpam-2346	239	22	of	of	ADP
ejpam-2346	239	23	the	the	DET
ejpam-2346	239	24	edges	edge	NOUN
ejpam-2346	239	25	of	of	ADP
ejpam-2346	239	26	the	the	DET
ejpam-2346	239	27	upper	upper	ADJ
ejpam-2346	239	28	portion	portion	NOUN
ejpam-2346	239	29	of	of	ADP
ejpam-2346	239	30	the	the	DET
ejpam-2346	239	31	heptahedron	heptahedron	NOUN
ejpam-2346	239	32	becomes	become	VERB
ejpam-2346	239	33	h′′1h	h′′1h	ADP
ejpam-2346	239	34	′′	′′	NOUN
ejpam-2346	239	35	7	7	NUM
ejpam-2346	239	36	=	=	SYM
ejpam-2346	239	37	2.6	2.6	NUM
ejpam-2346	239	38	,	,	PUNCT
ejpam-2346	239	39	h′′2h	h′′2h	X
ejpam-2346	239	40	′′	′′	PROPN
ejpam-2346	239	41	7	7	NUM
ejpam-2346	239	42	=	=	SYM
ejpam-2346	239	43	2	2	NUM
ejpam-2346	239	44	,	,	PUNCT
ejpam-2346	239	45	h′′3h	h′′3h	NOUN
ejpam-2346	239	46	′′	′′	PROPN
ejpam-2346	239	47	7	7	NUM
ejpam-2346	239	48	=	=	SYM
ejpam-2346	239	49	2	2	NUM
ejpam-2346	239	50	,	,	PUNCT
ejpam-2346	239	51	h′′4h	h′′4h	VERB
ejpam-2346	239	52	′′	′′	PROPN
ejpam-2346	239	53	7	7	NUM
ejpam-2346	239	54	=	=	SYM
ejpam-2346	239	55	2.6	2.6	NUM
ejpam-2346	239	56	,	,	PUNCT
ejpam-2346	239	57	h′′5h	h′′5h	PROPN
ejpam-2346	239	58	′′	′′	PROPN
ejpam-2346	239	59	7	7	NUM
ejpam-2346	239	60	=	=	SYM
ejpam-2346	239	61	2	2	NUM
ejpam-2346	239	62	,	,	PUNCT
ejpam-2346	239	63	h′′6h	h′′6h	DET
ejpam-2346	239	64	′′	′′	PROPN
ejpam-2346	239	65	7	7	NUM
ejpam-2346	239	66	=	=	SYM
ejpam-2346	239	67	2.2	2.2	NUM
ejpam-2346	239	68	.	.	PUNCT
ejpam-2346	240	1	so	so	ADV
ejpam-2346	240	2	,	,	PUNCT
ejpam-2346	240	3	we	we	PRON
ejpam-2346	240	4	observe	observe	VERB
ejpam-2346	240	5	that	that	SCONJ
ejpam-2346	240	6	the	the	DET
ejpam-2346	240	7	given	give	VERB
ejpam-2346	240	8	heptahedron	heptahedron	NOUN
ejpam-2346	240	9	converges	converge	NOUN
ejpam-2346	240	10	to	to	PART
ejpam-2346	240	11	regularize	regularize	VERB
ejpam-2346	240	12	and	and	CCONJ
ejpam-2346	240	13	it	it	PRON
ejpam-2346	240	14	becomes	become	VERB
ejpam-2346	240	15	a	a	DET
ejpam-2346	240	16	regular	regular	ADJ
ejpam-2346	240	17	heptahedron	heptahedron	NOUN
ejpam-2346	240	18	(	(	PUNCT
ejpam-2346	240	19	approximately	approximately	ADV
ejpam-2346	240	20	)	)	PUNCT
ejpam-2346	240	21	.	.	PUNCT
ejpam-2346	241	1	now	now	ADV
ejpam-2346	241	2	,	,	PUNCT
ejpam-2346	241	3	if	if	SCONJ
ejpam-2346	241	4	we	we	PRON
ejpam-2346	241	5	use	use	VERB
ejpam-2346	241	6	the	the	DET
ejpam-2346	241	7	transformation	transformation	NOUN
ejpam-2346	241	8	(	(	PUNCT
ejpam-2346	241	9	4	4	NUM
ejpam-2346	241	10	)	)	PUNCT
ejpam-2346	241	11	,	,	PUNCT
ejpam-2346	241	12	we	we	PRON
ejpam-2346	241	13	get	get	VERB
ejpam-2346	241	14	h′7	h′7	NOUN
ejpam-2346	241	15	=	=	PUNCT
ejpam-2346	241	16	(	(	PUNCT
ejpam-2346	241	17	3	3	NUM
ejpam-2346	241	18	,	,	PUNCT
ejpam-2346	241	19	4	4	NUM
ejpam-2346	241	20	,	,	PUNCT
ejpam-2346	241	21	4.9	4.9	NUM
ejpam-2346	241	22	)	)	PUNCT
ejpam-2346	241	23	.	.	PUNCT
ejpam-2346	242	1	and	and	CCONJ
ejpam-2346	242	2	after	after	ADP
ejpam-2346	242	3	the	the	DET
ejpam-2346	242	4	first	first	ADJ
ejpam-2346	242	5	step	step	NOUN
ejpam-2346	242	6	,	,	PUNCT
ejpam-2346	242	7	we	we	PRON
ejpam-2346	242	8	see	see	VERB
ejpam-2346	242	9	that	that	DET
ejpam-2346	242	10	length	length	NOUN
ejpam-2346	242	11	of	of	ADP
ejpam-2346	242	12	the	the	DET
ejpam-2346	242	13	edges	edge	NOUN
ejpam-2346	242	14	(	(	PUNCT
ejpam-2346	242	15	upper	upper	ADJ
ejpam-2346	242	16	portion	portion	NOUN
ejpam-2346	242	17	)	)	PUNCT
ejpam-2346	242	18	of	of	ADP
ejpam-2346	242	19	the	the	DET
ejpam-2346	242	20	given	give	VERB
ejpam-2346	242	21	heptahedron	heptahedron	NOUN
ejpam-2346	242	22	is	be	AUX
ejpam-2346	242	23	not	not	PART
ejpam-2346	242	24	equal	equal	ADJ
ejpam-2346	242	25	.	.	PUNCT
ejpam-2346	243	1	if	if	SCONJ
ejpam-2346	243	2	we	we	PRON
ejpam-2346	243	3	use	use	VERB
ejpam-2346	243	4	this	this	DET
ejpam-2346	243	5	transformation	transformation	NOUN
ejpam-2346	243	6	after	after	ADP
ejpam-2346	243	7	second	second	ADJ
ejpam-2346	243	8	step	step	NOUN
ejpam-2346	243	9	,	,	PUNCT
ejpam-2346	243	10	we	we	PRON
ejpam-2346	243	11	get	get	VERB
ejpam-2346	243	12	h′′7	h′′7	NOUN
ejpam-2346	243	13	=	=	SYM
ejpam-2346	243	14	(	(	PUNCT
ejpam-2346	243	15	3.3.5.3	3.3.5.3	NUM
ejpam-2346	243	16	,	,	PUNCT
ejpam-2346	243	17	6.6	6.6	NUM
ejpam-2346	243	18	)	)	PUNCT
ejpam-2346	243	19	and	and	CCONJ
ejpam-2346	243	20	we	we	PRON
ejpam-2346	243	21	observe	observe	VERB
ejpam-2346	243	22	also	also	ADV
ejpam-2346	243	23	that	that	SCONJ
ejpam-2346	243	24	the	the	DET
ejpam-2346	243	25	length	length	NOUN
ejpam-2346	243	26	of	of	ADP
ejpam-2346	243	27	the	the	DET
ejpam-2346	243	28	upper	upper	ADJ
ejpam-2346	243	29	portion	portion	NOUN
ejpam-2346	243	30	is	be	AUX
ejpam-2346	243	31	not	not	PART
ejpam-2346	243	32	regular	regular	ADJ
ejpam-2346	243	33	.	.	PUNCT
ejpam-2346	244	1	but	but	CCONJ
ejpam-2346	244	2	after	after	ADP
ejpam-2346	244	3	third	third	ADJ
ejpam-2346	244	4	step	step	NOUN
ejpam-2346	244	5	,	,	PUNCT
ejpam-2346	244	6	we	we	PRON
ejpam-2346	244	7	get	get	VERB
ejpam-2346	244	8	h′′′7	h′′′7	NOUN
ejpam-2346	244	9	=	=	SYM
ejpam-2346	244	10	(	(	PUNCT
ejpam-2346	244	11	3.2	3.2	NUM
ejpam-2346	244	12	,	,	PUNCT
ejpam-2346	244	13	4.9	4.9	NUM
ejpam-2346	244	14	,	,	PUNCT
ejpam-2346	244	15	6	6	NUM
ejpam-2346	244	16	)	)	PUNCT
ejpam-2346	244	17	and	and	CCONJ
ejpam-2346	244	18	we	we	PRON
ejpam-2346	244	19	see	see	VERB
ejpam-2346	244	20	that	that	DET
ejpam-2346	244	21	h′′′1	h′′′1	PROPN
ejpam-2346	244	22	h	h	NOUN
ejpam-2346	244	23	′′′	′′′	PROPN
ejpam-2346	244	24	7	7	NUM
ejpam-2346	244	25	=	=	SYM
ejpam-2346	244	26	.8	.8	PROPN
ejpam-2346	244	27	,	,	PUNCT
ejpam-2346	244	28	h′′′2	h′′′2	PROPN
ejpam-2346	244	29	h	h	NOUN
ejpam-2346	244	30	′′′	′′′	PROPN
ejpam-2346	244	31	7	7	NUM
ejpam-2346	244	32	=	=	SYM
ejpam-2346	244	33	.7	.7	PROPN
ejpam-2346	244	34	,	,	PUNCT
ejpam-2346	244	35	h′′′3	h′′′3	PROPN
ejpam-2346	244	36	h	h	NOUN
ejpam-2346	245	1	′′′	′′′	VERB
ejpam-2346	245	2	7	7	NUM
ejpam-2346	245	3	=	=	SYM
ejpam-2346	245	4	.8	.8	PROPN
ejpam-2346	245	5	,	,	PUNCT
ejpam-2346	245	6	h′′′4	h′′′4	PROPN
ejpam-2346	245	7	h	h	NOUN
ejpam-2346	245	8	′′′	′′′	PROPN
ejpam-2346	245	9	7	7	NUM
ejpam-2346	245	10	=	=	SYM
ejpam-2346	245	11	1	1	NUM
ejpam-2346	245	12	,	,	PUNCT
ejpam-2346	245	13	h′′′5	h′′′5	NOUN
ejpam-2346	246	1	h	h	NOUN
ejpam-2346	246	2	′′′	′′′	VERB
ejpam-2346	246	3	7	7	NUM
ejpam-2346	246	4	=	=	SYM
ejpam-2346	246	5	.8	.8	NUM
ejpam-2346	246	6	,	,	PUNCT
ejpam-2346	246	7	h′′′6	h′′′6	PROPN
ejpam-2346	246	8	h	h	NOUN
ejpam-2346	246	9	′′′	′′′	PROPN
ejpam-2346	246	10	7	7	NUM
ejpam-2346	246	11	=	=	SYM
ejpam-2346	246	12	.6	.6	NUM
ejpam-2346	246	13	.	.	PUNCT
ejpam-2346	247	1	so	so	ADV
ejpam-2346	247	2	,	,	PUNCT
ejpam-2346	247	3	we	we	PRON
ejpam-2346	247	4	see	see	VERB
ejpam-2346	247	5	that	that	SCONJ
ejpam-2346	247	6	it	it	PRON
ejpam-2346	247	7	tends	tend	VERB
ejpam-2346	247	8	to	to	PART
ejpam-2346	247	9	regularize	regularize	VERB
ejpam-2346	247	10	.	.	PUNCT
ejpam-2346	248	1	so	so	ADV
ejpam-2346	248	2	the	the	DET
ejpam-2346	248	3	deformed	deform	VERB
ejpam-2346	248	4	heptahedron	heptahedron	NOUN
ejpam-2346	248	5	becomes	become	VERB
ejpam-2346	248	6	a	a	DET
ejpam-2346	248	7	regular	regular	ADJ
ejpam-2346	248	8	heptahedron	heptahedron	NOUN
ejpam-2346	248	9	.	.	PUNCT
ejpam-2346	249	1	if	if	SCONJ
ejpam-2346	249	2	we	we	PRON
ejpam-2346	249	3	apply	apply	VERB
ejpam-2346	249	4	transformation	transformation	NOUN
ejpam-2346	249	5	(	(	PUNCT
ejpam-2346	249	6	5	5	NUM
ejpam-2346	249	7	)	)	PUNCT
ejpam-2346	249	8	after	after	ADP
ejpam-2346	249	9	first	first	ADJ
ejpam-2346	249	10	transformation	transformation	NOUN
ejpam-2346	249	11	of	of	ADP
ejpam-2346	249	12	(	(	PUNCT
ejpam-2346	249	13	4	4	NUM
ejpam-2346	249	14	)	)	PUNCT
ejpam-2346	249	15	on	on	ADP
ejpam-2346	249	16	heptahedron	heptahedron	NOUN
ejpam-2346	249	17	,	,	PUNCT
ejpam-2346	249	18	we	we	PRON
ejpam-2346	249	19	get	get	VERB
ejpam-2346	249	20	h′′1	h′′1	NOUN
ejpam-2346	249	21	=	=	SYM
ejpam-2346	249	22	c1	c1	PROPN
ejpam-2346	249	23	,	,	PUNCT
ejpam-2346	249	24	h	h	NOUN
ejpam-2346	249	25	′′	′′	PROPN
ejpam-2346	249	26	2	2	NUM
ejpam-2346	249	27	=	=	SYM
ejpam-2346	249	28	c2	c2	PROPN
ejpam-2346	249	29	,	,	PUNCT
ejpam-2346	249	30	h	h	NOUN
ejpam-2346	250	1	′′	′′	NOUN
ejpam-2346	250	2	3	3	NUM
ejpam-2346	250	3	=	=	SYM
ejpam-2346	250	4	c3	c3	PROPN
ejpam-2346	250	5	,	,	PUNCT
ejpam-2346	250	6	h	h	NOUN
ejpam-2346	250	7	′′	′′	PROPN
ejpam-2346	250	8	4	4	NUM
ejpam-2346	250	9	=	=	SYM
ejpam-2346	250	10	c4	c4	NOUN
ejpam-2346	250	11	,	,	PUNCT
ejpam-2346	250	12	h	h	NOUN
ejpam-2346	250	13	′′	′′	NOUN
ejpam-2346	250	14	5	5	NUM
ejpam-2346	250	15	=	=	SYM
ejpam-2346	250	16	c5	c5	PROPN
ejpam-2346	250	17	,	,	PUNCT
ejpam-2346	250	18	h	h	NOUN
ejpam-2346	250	19	′′	′′	PROPN
ejpam-2346	250	20	6	6	NUM
ejpam-2346	250	21	=	=	SYM
ejpam-2346	250	22	c6	c6	PROPN
ejpam-2346	250	23	and	and	CCONJ
ejpam-2346	250	24	h′′7	h′′7	NOUN
ejpam-2346	250	25	=	=	SYM
ejpam-2346	250	26	(	(	PUNCT
ejpam-2346	250	27	3.3	3.3	NUM
ejpam-2346	250	28	,	,	PUNCT
ejpam-2346	250	29	5.3	5.3	NUM
ejpam-2346	250	30	,	,	PUNCT
ejpam-2346	250	31	6.6	6.6	NUM
ejpam-2346	250	32	)	)	PUNCT
ejpam-2346	250	33	.	.	PUNCT
ejpam-2346	251	1	we	we	PRON
ejpam-2346	251	2	observe	observe	VERB
ejpam-2346	251	3	that	that	SCONJ
ejpam-2346	251	4	the	the	DET
ejpam-2346	251	5	length	length	NOUN
ejpam-2346	251	6	of	of	ADP
ejpam-2346	251	7	the	the	DET
ejpam-2346	251	8	upper	upper	ADJ
ejpam-2346	251	9	portion	portion	NOUN
ejpam-2346	251	10	h′′1h	h′′1h	VERB
ejpam-2346	251	11	′′	′′	NOUN
ejpam-2346	251	12	7	7	NUM
ejpam-2346	251	13	=	=	SYM
ejpam-2346	251	14	2.7	2.7	NUM
ejpam-2346	251	15	,	,	PUNCT
ejpam-2346	251	16	h′′2h	h′′2h	X
ejpam-2346	252	1	′′	′′	PROPN
ejpam-2346	252	2	7	7	NUM
ejpam-2346	252	3	=	=	SYM
ejpam-2346	252	4	2	2	NUM
ejpam-2346	252	5	,	,	PUNCT
ejpam-2346	252	6	h′′3h	h′′3h	NOUN
ejpam-2346	252	7	′′	′′	PROPN
ejpam-2346	252	8	7	7	NUM
ejpam-2346	252	9	=	=	SYM
ejpam-2346	252	10	2	2	NUM
ejpam-2346	252	11	,	,	PUNCT
ejpam-2346	252	12	h′′4h	h′′4h	VERB
ejpam-2346	252	13	′′	′′	PROPN
ejpam-2346	252	14	7	7	NUM
ejpam-2346	252	15	=	=	SYM
ejpam-2346	252	16	2.7	2.7	NUM
ejpam-2346	252	17	,	,	PUNCT
ejpam-2346	252	18	h′′5h	h′′5h	PROPN
ejpam-2346	252	19	′′	′′	PROPN
ejpam-2346	252	20	7	7	NUM
ejpam-2346	252	21	=	=	SYM
ejpam-2346	252	22	2	2	NUM
ejpam-2346	252	23	,	,	PUNCT
ejpam-2346	252	24	h′′6h	h′′6h	DET
ejpam-2346	252	25	′′	′′	PROPN
ejpam-2346	252	26	7	7	NUM
ejpam-2346	252	27	=	=	SYM
ejpam-2346	252	28	2	2	NUM
ejpam-2346	252	29	.	.	PUNCT
ejpam-2346	253	1	so	so	ADV
ejpam-2346	253	2	,	,	PUNCT
ejpam-2346	253	3	it	it	PRON
ejpam-2346	253	4	also	also	ADV
ejpam-2346	253	5	tends	tend	VERB
ejpam-2346	253	6	to	to	PART
ejpam-2346	253	7	regularize	regularize	VERB
ejpam-2346	253	8	(	(	PUNCT
ejpam-2346	253	9	approximately	approximately	ADV
ejpam-2346	253	10	)	)	PUNCT
ejpam-2346	253	11	.	.	PUNCT
ejpam-2346	254	1	all	all	DET
ejpam-2346	254	2	the	the	DET
ejpam-2346	254	3	above	above	ADJ
ejpam-2346	254	4	case	case	NOUN
ejpam-2346	254	5	the	the	DET
ejpam-2346	254	6	scaling	scale	VERB
ejpam-2346	254	7	factor	factor	NOUN
ejpam-2346	254	8	σ	σ	PROPN
ejpam-2346	254	9	=	=	SYM
ejpam-2346	254	10	.1	.1	PROPN
ejpam-2346	254	11	.	.	PUNCT
ejpam-2346	255	1	example	example	NOUN
ejpam-2346	255	2	12	12	NUM
ejpam-2346	255	3	.	.	PUNCT
ejpam-2346	256	1	now	now	ADV
ejpam-2346	256	2	,	,	PUNCT
ejpam-2346	256	3	we	we	PRON
ejpam-2346	256	4	use	use	VERB
ejpam-2346	256	5	transformation	transformation	NOUN
ejpam-2346	256	6	(	(	PUNCT
ejpam-2346	256	7	5	5	NUM
ejpam-2346	256	8	)	)	PUNCT
ejpam-2346	256	9	on	on	ADP
ejpam-2346	256	10	the	the	DET
ejpam-2346	256	11	example	example	NOUN
ejpam-2346	256	12	h1	h1	PROPN
ejpam-2346	256	13	≡	≡	PROPN
ejpam-2346	256	14	(	(	PUNCT
ejpam-2346	256	15	1	1	NUM
ejpam-2346	256	16	,	,	PUNCT
ejpam-2346	256	17	0	0	NUM
ejpam-2346	256	18	,	,	PUNCT
ejpam-2346	256	19	1	1	NUM
ejpam-2346	256	20	)	)	PUNCT
ejpam-2346	256	21	,	,	PUNCT
ejpam-2346	256	22	h2	h2	PROPN
ejpam-2346	256	23	≡	≡	PROPN
ejpam-2346	256	24	(	(	PUNCT
ejpam-2346	256	25	1	1	NUM
ejpam-2346	256	26	,	,	PUNCT
ejpam-2346	256	27	5	5	NUM
ejpam-2346	256	28	,	,	PUNCT
ejpam-2346	256	29	1	1	NUM
ejpam-2346	256	30	)	)	PUNCT
ejpam-2346	256	31	,	,	PUNCT
ejpam-2346	256	32	h3	h3	NOUN
ejpam-2346	256	33	≡	≡	PROPN
ejpam-2346	256	34	(	(	PUNCT
ejpam-2346	256	35	4	4	NUM
ejpam-2346	256	36	,	,	PUNCT
ejpam-2346	256	37	1	1	NUM
ejpam-2346	256	38	,	,	PUNCT
ejpam-2346	256	39	1	1	NUM
ejpam-2346	256	40	)	)	PUNCT
ejpam-2346	256	41	,	,	PUNCT
ejpam-2346	256	42	h4	h4	PROPN
ejpam-2346	256	43	≡	≡	PROPN
ejpam-2346	256	44	(	(	PUNCT
ejpam-2346	256	45	4	4	NUM
ejpam-2346	256	46	,	,	PUNCT
ejpam-2346	256	47	6	6	NUM
ejpam-2346	256	48	,	,	PUNCT
ejpam-2346	256	49	1	1	NUM
ejpam-2346	256	50	)	)	PUNCT
ejpam-2346	256	51	,	,	PUNCT
ejpam-2346	256	52	h5	h5	PROPN
ejpam-2346	256	53	≡	≡	PROPN
ejpam-2346	256	54	(	(	PUNCT
ejpam-2346	256	55	0	0	NUM
ejpam-2346	256	56	,	,	PUNCT
ejpam-2346	256	57	3	3	NUM
ejpam-2346	256	58	,	,	PUNCT
ejpam-2346	256	59	1	1	NUM
ejpam-2346	256	60	)	)	PUNCT
ejpam-2346	256	61	,	,	PUNCT
ejpam-2346	256	62	h6	h6	PROPN
ejpam-2346	256	63	≡	≡	PROPN
ejpam-2346	256	64	(	(	PUNCT
ejpam-2346	256	65	5	5	NUM
ejpam-2346	256	66	,	,	PUNCT
ejpam-2346	256	67	3	3	NUM
ejpam-2346	256	68	,	,	PUNCT
ejpam-2346	256	69	1	1	NUM
ejpam-2346	256	70	)	)	PUNCT
ejpam-2346	256	71	,	,	PUNCT
ejpam-2346	256	72	h7	h7	PROPN
ejpam-2346	256	73	≡	≡	PROPN
ejpam-2346	256	74	(	(	PUNCT
ejpam-2346	256	75	5	5	NUM
ejpam-2346	256	76	,	,	PUNCT
ejpam-2346	256	77	0	0	NUM
ejpam-2346	256	78	,	,	PUNCT
ejpam-2346	256	79	2	2	NUM
ejpam-2346	256	80	)	)	PUNCT
ejpam-2346	256	81	,	,	PUNCT
ejpam-2346	256	82	the	the	DET
ejpam-2346	256	83	transformed	transform	VERB
ejpam-2346	256	84	heptahedron	heptahedron	NOUN
ejpam-2346	256	85	becomes	become	VERB
ejpam-2346	256	86	h′1	h′1	ADJ
ejpam-2346	256	87	≡	≡	PROPN
ejpam-2346	256	88	(	(	PUNCT
ejpam-2346	256	89	1	1	NUM
ejpam-2346	256	90	,	,	PUNCT
ejpam-2346	256	91	0	0	NUM
ejpam-2346	256	92	,	,	PUNCT
ejpam-2346	256	93	1	1	NUM
ejpam-2346	256	94	)	)	PUNCT
ejpam-2346	256	95	,	,	PUNCT
ejpam-2346	256	96	h′2	h′2	PROPN
ejpam-2346	256	97	≡	≡	PROPN
ejpam-2346	256	98	(	(	PUNCT
ejpam-2346	256	99	1	1	NUM
ejpam-2346	256	100	,	,	PUNCT
ejpam-2346	256	101	5	5	NUM
ejpam-2346	256	102	,	,	PUNCT
ejpam-2346	256	103	1	1	NUM
ejpam-2346	256	104	)	)	PUNCT
ejpam-2346	256	105	,	,	PUNCT
ejpam-2346	256	106	h′3	h′3	NOUN
ejpam-2346	256	107	≡	≡	PROPN
ejpam-2346	256	108	(	(	PUNCT
ejpam-2346	256	109	4	4	NUM
ejpam-2346	256	110	,	,	PUNCT
ejpam-2346	256	111	1	1	NUM
ejpam-2346	256	112	,	,	PUNCT
ejpam-2346	256	113	1	1	NUM
ejpam-2346	256	114	)	)	PUNCT
ejpam-2346	256	115	,	,	PUNCT
ejpam-2346	256	116	h′4	h′4	NOUN
ejpam-2346	256	117	≡	≡	PROPN
ejpam-2346	256	118	(	(	PUNCT
ejpam-2346	256	119	4	4	NUM
ejpam-2346	256	120	,	,	PUNCT
ejpam-2346	256	121	6	6	NUM
ejpam-2346	256	122	,	,	PUNCT
ejpam-2346	256	123	1	1	NUM
ejpam-2346	256	124	)	)	PUNCT
ejpam-2346	256	125	,	,	PUNCT
ejpam-2346	256	126	h′5	h′5	NOUN
ejpam-2346	256	127	≡	≡	PROPN
ejpam-2346	256	128	(	(	PUNCT
ejpam-2346	256	129	0	0	NUM
ejpam-2346	256	130	,	,	PUNCT
ejpam-2346	256	131	3	3	NUM
ejpam-2346	256	132	,	,	PUNCT
ejpam-2346	256	133	1	1	NUM
ejpam-2346	256	134	)	)	PUNCT
ejpam-2346	256	135	,	,	PUNCT
ejpam-2346	256	136	h′6	h′6	ADJ
ejpam-2346	256	137	≡	≡	PROPN
ejpam-2346	256	138	(	(	PUNCT
ejpam-2346	256	139	5	5	NUM
ejpam-2346	256	140	,	,	PUNCT
ejpam-2346	256	141	3	3	NUM
ejpam-2346	256	142	,	,	PUNCT
ejpam-2346	256	143	1	1	NUM
ejpam-2346	256	144	)	)	PUNCT
ejpam-2346	256	145	and	and	CCONJ
ejpam-2346	256	146	h′7	h′7	X
ejpam-2346	256	147	≡	≡	PROPN
ejpam-2346	256	148	(	(	PUNCT
ejpam-2346	256	149	2.5	2.5	NUM
ejpam-2346	256	150	,	,	PUNCT
ejpam-2346	256	151	3	3	NUM
ejpam-2346	256	152	,	,	PUNCT
ejpam-2346	256	153	1.1	1.1	NUM
ejpam-2346	256	154	)	)	PUNCT
ejpam-2346	256	155	taking	take	VERB
ejpam-2346	256	156	scaling	scaling	NOUN
ejpam-2346	256	157	factor	factor	NOUN
ejpam-2346	256	158	σ	σ	NOUN
ejpam-2346	256	159	=	=	SYM
ejpam-2346	256	160	.1	.1	PROPN
ejpam-2346	256	161	and	and	CCONJ
ejpam-2346	256	162	the	the	DET
ejpam-2346	256	163	length	length	NOUN
ejpam-2346	256	164	of	of	ADP
ejpam-2346	256	165	the	the	DET
ejpam-2346	256	166	upper	upper	ADJ
ejpam-2346	256	167	portion	portion	NOUN
ejpam-2346	256	168	are	be	AUX
ejpam-2346	256	169	h′1h	h′1h	PROPN
ejpam-2346	256	170	′	′	NUM
ejpam-2346	256	171	7	7	NUM
ejpam-2346	256	172	=	=	SYM
ejpam-2346	256	173	3.3	3.3	NUM
ejpam-2346	256	174	,	,	PUNCT
ejpam-2346	256	175	h′2h	h′2h	PROPN
ejpam-2346	256	176	′	′	NUM
ejpam-2346	256	177	7	7	NUM
ejpam-2346	256	178	=	=	SYM
ejpam-2346	256	179	2.5	2.5	NUM
ejpam-2346	256	180	,	,	PUNCT
ejpam-2346	256	181	h′3h	h′3h	PROPN
ejpam-2346	256	182	′	′	NUM
ejpam-2346	256	183	7	7	NUM
ejpam-2346	256	184	=	=	SYM
ejpam-2346	256	185	2.5	2.5	NUM
ejpam-2346	256	186	,	,	PUNCT
ejpam-2346	256	187	h′4h	h′4h	NUM
ejpam-2346	256	188	′	′	NOUN
ejpam-2346	256	189	7	7	NUM
ejpam-2346	256	190	=	=	SYM
ejpam-2346	256	191	3.3	3.3	NUM
ejpam-2346	256	192	,	,	PUNCT
ejpam-2346	256	193	h′5h	h′5h	PROPN
ejpam-2346	256	194	′	′	NOUN
ejpam-2346	256	195	7	7	NUM
ejpam-2346	256	196	=	=	SYM
ejpam-2346	256	197	2.5	2.5	NUM
ejpam-2346	256	198	,	,	PUNCT
ejpam-2346	256	199	h′6h	h′6h	PROPN
ejpam-2346	256	200	′	′	NOUN
ejpam-2346	256	201	7	7	NUM
ejpam-2346	256	202	=	=	SYM
ejpam-2346	256	203	2.5	2.5	NUM
ejpam-2346	256	204	.	.	PUNCT
ejpam-2346	257	1	from	from	ADP
ejpam-2346	257	2	this	this	PRON
ejpam-2346	257	3	it	it	PRON
ejpam-2346	257	4	is	be	AUX
ejpam-2346	257	5	clear	clear	ADJ
ejpam-2346	257	6	that	that	SCONJ
ejpam-2346	257	7	this	this	PRON
ejpam-2346	257	8	transformed	transform	VERB
ejpam-2346	257	9	heptahedron	heptahedron	NOUN
ejpam-2346	257	10	converges	converge	NOUN
ejpam-2346	257	11	to	to	ADP
ejpam-2346	257	12	regular	regular	ADJ
ejpam-2346	257	13	(	(	PUNCT
ejpam-2346	257	14	approx	approx	PROPN
ejpam-2346	257	15	)	)	PUNCT
ejpam-2346	257	16	.	.	PUNCT
ejpam-2346	258	1	from	from	ADP
ejpam-2346	258	2	the	the	DET
ejpam-2346	258	3	above	above	ADJ
ejpam-2346	258	4	examples	example	NOUN
ejpam-2346	258	5	we	we	PRON
ejpam-2346	258	6	observe	observe	VERB
ejpam-2346	258	7	that	that	SCONJ
ejpam-2346	258	8	the	the	DET
ejpam-2346	258	9	transformation	transformation	NOUN
ejpam-2346	258	10	(	(	PUNCT
ejpam-2346	258	11	5	5	X
ejpam-2346	258	12	)	)	PUNCT
ejpam-2346	258	13	plays	play	VERB
ejpam-2346	258	14	an	an	DET
ejpam-2346	258	15	important	important	ADJ
ejpam-2346	258	16	role	role	NOUN
ejpam-2346	258	17	to	to	PART
ejpam-2346	258	18	regularize	regularize	VERB
ejpam-2346	258	19	the	the	DET
ejpam-2346	258	20	heptahedron	heptahedron	NOUN
ejpam-2346	258	21	.	.	PUNCT
ejpam-2346	259	1	6	6	NUM
ejpam-2346	259	2	.	.	X
ejpam-2346	259	3	characterization	characterization	NOUN
ejpam-2346	259	4	of	of	ADP
ejpam-2346	259	5	energy	energy	NOUN
ejpam-2346	259	6	function	function	NOUN
ejpam-2346	259	7	of	of	ADP
ejpam-2346	259	8	a	a	DET
ejpam-2346	259	9	particular	particular	ADJ
ejpam-2346	259	10	type	type	NOUN
ejpam-2346	259	11	of	of	ADP
ejpam-2346	259	12	heptahedron	heptahedron	NOUN
ejpam-2346	259	13	using	use	VERB
ejpam-2346	259	14	getme	getme	NOUN
ejpam-2346	259	15	and	and	CCONJ
ejpam-2346	259	16	bdame	bdame	VERB
ejpam-2346	259	17	the	the	DET
ejpam-2346	259	18	changing	change	VERB
ejpam-2346	259	19	cost	cost	NOUN
ejpam-2346	259	20	function	function	NOUN
ejpam-2346	259	21	,	,	PUNCT
ejpam-2346	259	22	after	after	ADP
ejpam-2346	259	23	transforming	transform	VERB
ejpam-2346	259	24	the	the	DET
ejpam-2346	259	25	heptahedron	heptahedron	NOUN
ejpam-2346	259	26	by	by	ADP
ejpam-2346	259	27	getme	getme	NOUN
ejpam-2346	259	28	,	,	PUNCT
ejpam-2346	259	29	is	be	AUX
ejpam-2346	259	30	given	give	VERB
ejpam-2346	259	31	by	by	ADP
ejpam-2346	259	32	f(σh	f(σh	NOUN
ejpam-2346	259	33	)	)	PUNCT
ejpam-2346	260	1	=	=	PRON
ejpam-2346	260	2	|fhk	|fhk	NOUN
ejpam-2346	260	3	(	(	PUNCT
ejpam-2346	260	4	σn	σn	NOUN
ejpam-2346	260	5	)	)	PUNCT
ejpam-2346	260	6	∼	∼	NOUN
ejpam-2346	260	7	fhk+1	fhk+1	NOUN
ejpam-2346	260	8	(	(	PUNCT
ejpam-2346	260	9	σn)|	σn)|	AUX
ejpam-2346	260	10	now	now	ADV
ejpam-2346	260	11	using	use	VERB
ejpam-2346	260	12	bdame	bdame	NOUN
ejpam-2346	260	13	we	we	PRON
ejpam-2346	260	14	find	find	VERB
ejpam-2346	260	15	the	the	DET
ejpam-2346	260	16	numerical	numerical	ADJ
ejpam-2346	260	17	values	value	NOUN
ejpam-2346	260	18	of	of	ADP
ejpam-2346	260	19	changing	change	VERB
ejpam-2346	260	20	cost	cost	NOUN
ejpam-2346	260	21	function	function	NOUN
ejpam-2346	260	22	.	.	PUNCT
ejpam-2346	261	1	we	we	PRON
ejpam-2346	261	2	can	can	AUX
ejpam-2346	261	3	calculate	calculate	VERB
ejpam-2346	261	4	the	the	DET
ejpam-2346	261	5	changing	change	VERB
ejpam-2346	261	6	cost	cost	NOUN
ejpam-2346	261	7	function	function	NOUN
ejpam-2346	261	8	of	of	ADP
ejpam-2346	261	9	the	the	DET
ejpam-2346	261	10	heptahedron	heptahedron	NOUN
ejpam-2346	261	11	provided	provide	VERB
ejpam-2346	261	12	after	after	ADP
ejpam-2346	261	13	transformation	transformation	NOUN
ejpam-2346	261	14	the	the	DET
ejpam-2346	261	15	base	base	NOUN
ejpam-2346	261	16	points	point	NOUN
ejpam-2346	261	17	are	be	AUX
ejpam-2346	261	18	coplanar	coplanar	ADJ
ejpam-2346	261	19	.	.	PUNCT
ejpam-2346	262	1	let	let	VERB
ejpam-2346	262	2	us	we	PRON
ejpam-2346	262	3	consider	consider	VERB
ejpam-2346	262	4	an	an	DET
ejpam-2346	262	5	example	example	NOUN
ejpam-2346	262	6	where	where	SCONJ
ejpam-2346	262	7	h1	h1	PROPN
ejpam-2346	262	8	≡	≡	PROPN
ejpam-2346	262	9	(	(	PUNCT
ejpam-2346	262	10	5	5	NUM
ejpam-2346	262	11	,	,	PUNCT
ejpam-2346	262	12	2	2	NUM
ejpam-2346	262	13	,	,	PUNCT
ejpam-2346	262	14	5	5	NUM
ejpam-2346	262	15	)	)	PUNCT
ejpam-2346	262	16	,	,	PUNCT
ejpam-2346	262	17	h2	h2	PROPN
ejpam-2346	262	18	≡	≡	PROPN
ejpam-2346	262	19	(	(	PUNCT
ejpam-2346	262	20	5	5	NUM
ejpam-2346	262	21	,	,	PUNCT
ejpam-2346	262	22	7	7	NUM
ejpam-2346	262	23	,	,	PUNCT
ejpam-2346	262	24	5	5	NUM
ejpam-2346	262	25	)	)	PUNCT
ejpam-2346	262	26	,	,	PUNCT
ejpam-2346	262	27	h3	h3	NOUN
ejpam-2346	262	28	≡	≡	PROPN
ejpam-2346	262	29	(	(	PUNCT
ejpam-2346	262	30	0	0	NUM
ejpam-2346	262	31	,	,	PUNCT
ejpam-2346	262	32	7	7	NUM
ejpam-2346	262	33	,	,	PUNCT
ejpam-2346	262	34	5	5	NUM
ejpam-2346	262	35	)	)	PUNCT
ejpam-2346	262	36	,	,	PUNCT
ejpam-2346	262	37	h4	h4	PROPN
ejpam-2346	262	38	≡	≡	PROPN
ejpam-2346	262	39	(	(	PUNCT
ejpam-2346	262	40	4	4	NUM
ejpam-2346	262	41	,	,	PUNCT
ejpam-2346	262	42	4	4	NUM
ejpam-2346	262	43	,	,	PUNCT
ejpam-2346	262	44	5	5	NUM
ejpam-2346	262	45	)	)	PUNCT
ejpam-2346	262	46	,	,	PUNCT
ejpam-2346	262	47	h5	h5	PROPN
ejpam-2346	262	48	≡	≡	PROPN
ejpam-2346	262	49	(	(	PUNCT
ejpam-2346	262	50	0	0	NUM
ejpam-2346	262	51	,	,	PUNCT
ejpam-2346	262	52	1	1	NUM
ejpam-2346	262	53	,	,	PUNCT
ejpam-2346	262	54	5	5	NUM
ejpam-2346	262	55	)	)	PUNCT
ejpam-2346	262	56	,	,	PUNCT
ejpam-2346	262	57	h6	h6	PROPN
ejpam-2346	262	58	≡	≡	PROPN
ejpam-2346	262	59	(	(	PUNCT
ejpam-2346	262	60	5	5	NUM
ejpam-2346	262	61	,	,	PUNCT
ejpam-2346	262	62	1	1	NUM
ejpam-2346	262	63	,	,	PUNCT
ejpam-2346	262	64	5	5	NUM
ejpam-2346	262	65	)	)	PUNCT
ejpam-2346	262	66	are	be	AUX
ejpam-2346	262	67	the	the	DET
ejpam-2346	262	68	base	base	NOUN
ejpam-2346	262	69	points	point	NOUN
ejpam-2346	262	70	and	and	CCONJ
ejpam-2346	262	71	h7	h7	PROPN
ejpam-2346	262	72	≡	≡	PROPN
ejpam-2346	262	73	(	(	PUNCT
ejpam-2346	262	74	4	4	NUM
ejpam-2346	262	75	,	,	PUNCT
ejpam-2346	262	76	5	5	NUM
ejpam-2346	262	77	,	,	PUNCT
ejpam-2346	262	78	8)	8)	NUM
ejpam-2346	262	79	denote	denote	VERB
ejpam-2346	262	80	the	the	DET
ejpam-2346	262	81	apex	apex	NOUN
ejpam-2346	262	82	of	of	ADP
ejpam-2346	262	83	the	the	DET
ejpam-2346	262	84	the	the	DET
ejpam-2346	262	85	heptahedron	heptahedron	NOUN
ejpam-2346	262	86	.	.	PUNCT
ejpam-2346	263	1	here	here	ADV
ejpam-2346	263	2	,	,	PUNCT
ejpam-2346	263	3	(	(	PUNCT
ejpam-2346	263	4	2.5	2.5	NUM
ejpam-2346	263	5	,	,	PUNCT
ejpam-2346	263	6	4	4	NUM
ejpam-2346	263	7	,	,	PUNCT
ejpam-2346	263	8	5	5	NUM
ejpam-2346	263	9	)	)	PUNCT
ejpam-2346	263	10	be	be	AUX
ejpam-2346	263	11	the	the	DET
ejpam-2346	263	12	inters	inter	NOUN
ejpam-2346	263	13	.	.	PUNCT
ejpam-2346	264	1	dey	dey	PROPN
ejpam-2346	264	2	,	,	PUNCT
ejpam-2346	264	3	b.	b.	PROPN
ejpam-2346	264	4	pal	pal	PROPN
ejpam-2346	264	5	,	,	PUNCT
ejpam-2346	264	6	a.	a.	NOUN
ejpam-2346	264	7	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	264	8	/	/	SYM
ejpam-2346	264	9	eur	eur	PROPN
ejpam-2346	264	10	.	.	PUNCT
ejpam-2346	265	1	j.	j.	PROPN
ejpam-2346	265	2	pure	pure	PROPN
ejpam-2346	265	3	appl	appl	PROPN
ejpam-2346	265	4	.	.	PROPN
ejpam-2346	265	5	math	math	PROPN
ejpam-2346	265	6	,	,	PUNCT
ejpam-2346	265	7	11	11	NUM
ejpam-2346	265	8	(	(	PUNCT
ejpam-2346	265	9	1	1	NUM
ejpam-2346	265	10	)	)	PUNCT
ejpam-2346	265	11	(	(	PUNCT
ejpam-2346	265	12	2018	2018	NUM
ejpam-2346	265	13	)	)	PUNCT
ejpam-2346	265	14	,	,	PUNCT
ejpam-2346	265	15	315	315	NUM
ejpam-2346	265	16	-	-	SYM
ejpam-2346	265	17	330	330	NUM
ejpam-2346	265	18	327	327	NUM
ejpam-2346	265	19	secting	secte	VERB
ejpam-2346	265	20	point	point	NOUN
ejpam-2346	265	21	of	of	ADP
ejpam-2346	265	22	the	the	DET
ejpam-2346	265	23	base	base	ADJ
ejpam-2346	265	24	diagonals	diagonal	NOUN
ejpam-2346	265	25	of	of	ADP
ejpam-2346	265	26	the	the	DET
ejpam-2346	265	27	square	square	ADJ
ejpam-2346	265	28	part	part	NOUN
ejpam-2346	265	29	of	of	ADP
ejpam-2346	265	30	the	the	DET
ejpam-2346	265	31	heptahedron	heptahedron	NOUN
ejpam-2346	265	32	.	.	PUNCT
ejpam-2346	266	1	it	it	PRON
ejpam-2346	266	2	has	have	AUX
ejpam-2346	266	3	shown	show	VERB
ejpam-2346	266	4	in	in	ADP
ejpam-2346	266	5	the	the	DET
ejpam-2346	266	6	following	follow	VERB
ejpam-2346	266	7	figure	figure	NOUN
ejpam-2346	266	8	fig.3	fig.3	ADJ
ejpam-2346	266	9	:	:	PUNCT
ejpam-2346	266	10	characterization	characterization	NOUN
ejpam-2346	266	11	of	of	ADP
ejpam-2346	266	12	heptahedron	heptahedron	NOUN
ejpam-2346	266	13	using	use	VERB
ejpam-2346	266	14	bdame	bdame	NOUN
ejpam-2346	266	15	.	.	PUNCT
ejpam-2346	267	1	after	after	ADP
ejpam-2346	267	2	calculation	calculation	NOUN
ejpam-2346	267	3	,	,	PUNCT
ejpam-2346	267	4	we	we	PRON
ejpam-2346	267	5	get	get	VERB
ejpam-2346	267	6	apex	apex	NOUN
ejpam-2346	267	7	transformations	transformation	NOUN
ejpam-2346	267	8	initial	initial	ADJ
ejpam-2346	267	9	step	step	NOUN
ejpam-2346	267	10	2nd	2nd	ADJ
ejpam-2346	267	11	step	step	NOUN
ejpam-2346	267	12	3rd	3rd	ADJ
ejpam-2346	267	13	step	step	NOUN
ejpam-2346	267	14	4th	4th	ADJ
ejpam-2346	267	15	step	step	NOUN
ejpam-2346	267	16	fhk	fhk	VERB
ejpam-2346	267	17	(	(	PUNCT
ejpam-2346	267	18	σn	σn	NOUN
ejpam-2346	267	19	)	)	PUNCT
ejpam-2346	267	20	0.6999	0.6999	NUM
ejpam-2346	267	21	0.7251	0.7251	NUM
ejpam-2346	267	22	0.7507	0.7507	NUM
ejpam-2346	267	23	0.7770	0.7770	NUM
ejpam-2346	267	24	by	by	ADP
ejpam-2346	267	25	this	this	DET
ejpam-2346	267	26	example	example	NOUN
ejpam-2346	267	27	we	we	PRON
ejpam-2346	267	28	can	can	AUX
ejpam-2346	267	29	show	show	VERB
ejpam-2346	267	30	that	that	SCONJ
ejpam-2346	267	31	the	the	DET
ejpam-2346	267	32	heptahedron	heptahedron	NOUN
ejpam-2346	267	33	converges	converge	VERB
ejpam-2346	267	34	to	to	PART
ejpam-2346	267	35	regularize	regularize	VERB
ejpam-2346	267	36	on	on	ADP
ejpam-2346	267	37	the	the	DET
ejpam-2346	267	38	transformation	transformation	NOUN
ejpam-2346	267	39	(	(	PUNCT
ejpam-2346	267	40	2	2	NUM
ejpam-2346	267	41	)	)	PUNCT
ejpam-2346	267	42	.	.	PUNCT
ejpam-2346	268	1	we	we	PRON
ejpam-2346	268	2	see	see	VERB
ejpam-2346	268	3	in	in	ADP
ejpam-2346	268	4	figure	figure	NOUN
ejpam-2346	268	5	(	(	PUNCT
ejpam-2346	268	6	4	4	NUM
ejpam-2346	268	7	)	)	PUNCT
ejpam-2346	268	8	that	that	SCONJ
ejpam-2346	268	9	the	the	DET
ejpam-2346	268	10	values	value	NOUN
ejpam-2346	268	11	of	of	ADP
ejpam-2346	268	12	the	the	DET
ejpam-2346	268	13	changing	change	VERB
ejpam-2346	268	14	cost	cost	NOUN
ejpam-2346	268	15	function	function	NOUN
ejpam-2346	268	16	f(σh	f(σh	NOUN
ejpam-2346	268	17	)	)	PUNCT
ejpam-2346	268	18	are	be	AUX
ejpam-2346	268	19	0.0252	0.0252	NUM
ejpam-2346	268	20	,	,	PUNCT
ejpam-2346	268	21	0.0257	0.0257	NUM
ejpam-2346	268	22	and	and	CCONJ
ejpam-2346	268	23	0.0263	0.0263	NUM
ejpam-2346	268	24	.	.	PUNCT
ejpam-2346	269	1	references	reference	NOUN
ejpam-2346	269	2	328	328	NUM
ejpam-2346	269	3	0.69	0.69	NUM
ejpam-2346	269	4	0.7	0.7	NUM
ejpam-2346	269	5	0.71	0.71	NUM
ejpam-2346	269	6	0.72	0.72	NUM
ejpam-2346	269	7	0.73	0.73	NUM
ejpam-2346	269	8	0.74	0.74	NUM
ejpam-2346	269	9	0.75	0.75	NUM
ejpam-2346	269	10	0.76	0.76	NUM
ejpam-2346	269	11	0.77	0.77	NUM
ejpam-2346	269	12	0.78	0.78	NUM
ejpam-2346	269	13	0.0252	0.0252	NUM
ejpam-2346	269	14	0.0254	0.0254	NUM
ejpam-2346	269	15	0.0256	0.0256	NUM
ejpam-2346	269	16	0.0258	0.0258	NUM
ejpam-2346	269	17	0.026	0.026	NUM
ejpam-2346	269	18	0.0262	0.0262	NUM
ejpam-2346	269	19	0.0264	0.0264	NUM
ejpam-2346	269	20	0.0266	0.0266	NUM
ejpam-2346	269	21	0.0268	0.0268	NUM
ejpam-2346	269	22	0.027	0.027	NUM
ejpam-2346	269	23	f	f	PROPN
ejpam-2346	269	24	hk	hk	PROPN
ejpam-2346	269	25	(	(	PUNCT
ejpam-2346	269	26	σn	σn	PROPN
ejpam-2346	269	27	)	)	PUNCT
ejpam-2346	269	28	f	f	PROPN
ejpam-2346	269	29	(	(	PUNCT
ejpam-2346	269	30	σ	σ	PROPN
ejpam-2346	269	31	h	h	PROPN
ejpam-2346	269	32	)	)	PUNCT
ejpam-2346	270	1	fig.4	fig.4	VERB
ejpam-2346	270	2	:	:	PUNCT
ejpam-2346	270	3	changing	change	VERB
ejpam-2346	270	4	cost	cost	NOUN
ejpam-2346	270	5	function	function	NOUN
ejpam-2346	270	6	.	.	PUNCT
ejpam-2346	271	1	therefore	therefore	ADV
ejpam-2346	271	2	for	for	ADP
ejpam-2346	271	3	this	this	DET
ejpam-2346	271	4	example	example	NOUN
ejpam-2346	271	5	we	we	PRON
ejpam-2346	271	6	see	see	VERB
ejpam-2346	271	7	that	that	SCONJ
ejpam-2346	271	8	when	when	SCONJ
ejpam-2346	271	9	it	it	PRON
ejpam-2346	271	10	converges	converge	VERB
ejpam-2346	271	11	to	to	PART
ejpam-2346	271	12	regularize	regularize	VERB
ejpam-2346	271	13	,	,	PUNCT
ejpam-2346	271	14	the	the	DET
ejpam-2346	271	15	changing	change	VERB
ejpam-2346	271	16	cost	cost	NOUN
ejpam-2346	271	17	function	function	NOUN
ejpam-2346	271	18	also	also	ADV
ejpam-2346	271	19	increases	increase	VERB
ejpam-2346	271	20	.	.	PUNCT
ejpam-2346	272	1	one	one	PRON
ejpam-2346	272	2	can	can	AUX
ejpam-2346	272	3	also	also	ADV
ejpam-2346	272	4	calculate	calculate	VERB
ejpam-2346	272	5	the	the	DET
ejpam-2346	272	6	changing	change	VERB
ejpam-2346	272	7	cost	cost	NOUN
ejpam-2346	272	8	function	function	NOUN
ejpam-2346	272	9	for	for	ADP
ejpam-2346	272	10	any	any	DET
ejpam-2346	272	11	arbitrary	arbitrary	ADJ
ejpam-2346	272	12	heptahedron	heptahedron	NOUN
ejpam-2346	272	13	(	(	PUNCT
ejpam-2346	272	14	using	use	VERB
ejpam-2346	272	15	the	the	DET
ejpam-2346	272	16	method	method	NOUN
ejpam-2346	272	17	(	(	PUNCT
ejpam-2346	272	18	1	1	NUM
ejpam-2346	272	19	)	)	PUNCT
ejpam-2346	272	20	and	and	CCONJ
ejpam-2346	272	21	(	(	PUNCT
ejpam-2346	272	22	3	3	NUM
ejpam-2346	272	23	)	)	PUNCT
ejpam-2346	272	24	)	)	PUNCT
ejpam-2346	272	25	provided	provide	VERB
ejpam-2346	272	26	after	after	ADP
ejpam-2346	272	27	transformations	transformation	NOUN
ejpam-2346	272	28	the	the	DET
ejpam-2346	272	29	base	base	NOUN
ejpam-2346	272	30	points	point	NOUN
ejpam-2346	272	31	are	be	AUX
ejpam-2346	272	32	coplanar	coplanar	ADJ
ejpam-2346	272	33	.	.	PUNCT
ejpam-2346	273	1	7	7	X
ejpam-2346	273	2	.	.	X
ejpam-2346	273	3	conclusion	conclusion	NOUN
ejpam-2346	273	4	one	one	PRON
ejpam-2346	273	5	can	can	AUX
ejpam-2346	273	6	regularize	regularize	VERB
ejpam-2346	273	7	any	any	DET
ejpam-2346	273	8	3	3	NUM
ejpam-2346	273	9	-	-	PUNCT
ejpam-2346	273	10	d	d	NUM
ejpam-2346	273	11	figures	figure	NOUN
ejpam-2346	273	12	,	,	PUNCT
ejpam-2346	273	13	which	which	PRON
ejpam-2346	273	14	are	be	AUX
ejpam-2346	273	15	not	not	PART
ejpam-2346	273	16	simplex	simplex	NOUN
ejpam-2346	273	17	,	,	PUNCT
ejpam-2346	273	18	using	use	VERB
ejpam-2346	273	19	getme	getme	NOUN
ejpam-2346	273	20	and	and	CCONJ
ejpam-2346	273	21	bdame	bdame	NOUN
ejpam-2346	273	22	.	.	PUNCT
ejpam-2346	274	1	acknowledgements	acknowledgement	NOUN
ejpam-2346	274	2	the	the	DET
ejpam-2346	274	3	authors	author	NOUN
ejpam-2346	274	4	wish	wish	VERB
ejpam-2346	274	5	to	to	PART
ejpam-2346	274	6	express	express	VERB
ejpam-2346	274	7	their	their	PRON
ejpam-2346	274	8	sincere	sincere	ADJ
ejpam-2346	274	9	thanks	thank	NOUN
ejpam-2346	274	10	and	and	CCONJ
ejpam-2346	274	11	gratitude	gratitude	NOUN
ejpam-2346	274	12	to	to	ADP
ejpam-2346	274	13	the	the	DET
ejpam-2346	274	14	referee	referee	NOUN
ejpam-2346	274	15	for	for	ADP
ejpam-2346	274	16	valuable	valuable	ADJ
ejpam-2346	274	17	suggestions	suggestion	NOUN
ejpam-2346	274	18	towards	towards	ADP
ejpam-2346	274	19	the	the	DET
ejpam-2346	274	20	improvement	improvement	NOUN
ejpam-2346	274	21	of	of	ADP
ejpam-2346	274	22	the	the	DET
ejpam-2346	274	23	paper	paper	NOUN
ejpam-2346	274	24	.	.	PUNCT
ejpam-2346	275	1	the	the	DET
ejpam-2346	275	2	first	first	ADJ
ejpam-2346	275	3	author	author	NOUN
ejpam-2346	275	4	is	be	AUX
ejpam-2346	275	5	supported	support	VERB
ejpam-2346	275	6	by	by	ADP
ejpam-2346	275	7	dst	dst	PROPN
ejpam-2346	275	8	/	/	SYM
ejpam-2346	275	9	inspire	inspire	NOUN
ejpam-2346	275	10	fellowship/2013/1041	fellowship/2013/1041	NOUN
ejpam-2346	275	11	,	,	PUNCT
ejpam-2346	275	12	govt	govt	NOUN
ejpam-2346	275	13	.	.	PUNCT
ejpam-2346	276	1	of	of	ADP
ejpam-2346	276	2	india	india	PROPN
ejpam-2346	276	3	.	.	PUNCT
ejpam-2346	277	1	references	reference	NOUN
ejpam-2346	278	1	[	[	X
ejpam-2346	278	2	1	1	X
ejpam-2346	278	3	]	]	X
ejpam-2346	278	4	arindam	arindam	PROPN
ejpam-2346	278	5	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	278	6	and	and	CCONJ
ejpam-2346	278	7	buddhadev	buddhadev	PROPN
ejpam-2346	278	8	pal	pal	NOUN
ejpam-2346	278	9	.	.	PUNCT
ejpam-2346	279	1	quality	quality	NOUN
ejpam-2346	279	2	statistics	statistic	NOUN
ejpam-2346	279	3	of	of	ADP
ejpam-2346	279	4	octahedron	octahedron	NOUN
ejpam-2346	279	5	and	and	CCONJ
ejpam-2346	279	6	decahedron	decahedron	NOUN
ejpam-2346	279	7	with	with	ADP
ejpam-2346	279	8	the	the	DET
ejpam-2346	279	9	help	help	NOUN
ejpam-2346	279	10	of	of	ADP
ejpam-2346	279	11	c	c	NOUN
ejpam-2346	279	12	-	-	PUNCT
ejpam-2346	279	13	programs	program	NOUN
ejpam-2346	279	14	.	.	PUNCT
ejpam-2346	280	1	int	int	NOUN
ejpam-2346	280	2	.	.	PUNCT
ejpam-2346	281	1	j.	j.	PROPN
ejpam-2346	281	2	pure	pure	PROPN
ejpam-2346	281	3	appl	appl	PROPN
ejpam-2346	281	4	.	.	PUNCT
ejpam-2346	282	1	sci	sci	PROPN
ejpam-2346	282	2	.	.	PROPN
ejpam-2346	282	3	technol	technol	PROPN
ejpam-2346	282	4	,	,	PUNCT
ejpam-2346	282	5	1(2):26–41	1(2):26–41	NUM
ejpam-2346	282	6	,	,	PUNCT
ejpam-2346	282	7	2010	2010	NUM
ejpam-2346	282	8	.	.	PUNCT
ejpam-2346	283	1	[	[	X
ejpam-2346	283	2	2	2	NUM
ejpam-2346	283	3	]	]	PUNCT
ejpam-2346	283	4	jm	jm	PROPN
ejpam-2346	283	5	escobar	escobar	PROPN
ejpam-2346	283	6	,	,	PUNCT
ejpam-2346	283	7	e	e	NOUN
ejpam-2346	283	8	rodrıguez	rodrıguez	NOUN
ejpam-2346	283	9	,	,	PUNCT
ejpam-2346	283	10	r	r	NOUN
ejpam-2346	283	11	montenegro	montenegro	PROPN
ejpam-2346	283	12	,	,	PUNCT
ejpam-2346	283	13	g	g	PROPN
ejpam-2346	283	14	montero	montero	NOUN
ejpam-2346	283	15	,	,	PUNCT
ejpam-2346	283	16	and	and	CCONJ
ejpam-2346	283	17	jm	jm	PROPN
ejpam-2346	283	18	gonzález	gonzález	PROPN
ejpam-2346	283	19	-	-	PUNCT
ejpam-2346	283	20	yuste	yuste	NOUN
ejpam-2346	283	21	.	.	PUNCT
ejpam-2346	283	22	sireferences	sireference	NOUN
ejpam-2346	283	23	329	329	NUM
ejpam-2346	283	24	multaneous	multaneous	ADJ
ejpam-2346	283	25	untangling	untangling	NOUN
ejpam-2346	283	26	and	and	CCONJ
ejpam-2346	283	27	smoothing	smoothing	NOUN
ejpam-2346	283	28	of	of	ADP
ejpam-2346	283	29	tetrahedral	tetrahedral	ADJ
ejpam-2346	283	30	meshes	mesh	NOUN
ejpam-2346	283	31	.	.	PUNCT
ejpam-2346	284	1	computer	computer	NOUN
ejpam-2346	284	2	methods	method	NOUN
ejpam-2346	284	3	in	in	ADP
ejpam-2346	284	4	applied	applied	ADJ
ejpam-2346	284	5	mechanics	mechanic	NOUN
ejpam-2346	284	6	and	and	CCONJ
ejpam-2346	284	7	engineering	engineering	NOUN
ejpam-2346	284	8	,	,	PUNCT
ejpam-2346	284	9	192(25):2775–2787	192(25):2775–2787	NUM
ejpam-2346	284	10	,	,	PUNCT
ejpam-2346	284	11	2003	2003	NUM
ejpam-2346	284	12	.	.	PUNCT
ejpam-2346	285	1	[	[	X
ejpam-2346	285	2	3	3	X
ejpam-2346	285	3	]	]	X
ejpam-2346	285	4	lori	lori	PROPN
ejpam-2346	285	5	a	a	DET
ejpam-2346	285	6	freitag	freitag	NOUN
ejpam-2346	285	7	and	and	CCONJ
ejpam-2346	285	8	patrick	patrick	PROPN
ejpam-2346	285	9	m	m	PROPN
ejpam-2346	285	10	knupp	knupp	PROPN
ejpam-2346	285	11	.	.	PUNCT
ejpam-2346	286	1	tetrahedral	tetrahedral	ADJ
ejpam-2346	286	2	element	element	NOUN
ejpam-2346	286	3	shape	shape	NOUN
ejpam-2346	286	4	optimization	optimization	NOUN
ejpam-2346	286	5	via	via	ADP
ejpam-2346	286	6	the	the	DET
ejpam-2346	286	7	jacobian	jacobian	ADJ
ejpam-2346	286	8	determinant	determinant	ADJ
ejpam-2346	286	9	and	and	CCONJ
ejpam-2346	286	10	condition	condition	NOUN
ejpam-2346	286	11	number	number	NOUN
ejpam-2346	286	12	.	.	PUNCT
ejpam-2346	287	1	in	in	ADP
ejpam-2346	287	2	imr	imr	PROPN
ejpam-2346	287	3	,	,	PUNCT
ejpam-2346	287	4	pages	page	NOUN
ejpam-2346	287	5	247–258	247–258	NUM
ejpam-2346	287	6	,	,	PUNCT
ejpam-2346	287	7	1999	1999	NUM
ejpam-2346	287	8	.	.	PUNCT
ejpam-2346	288	1	[	[	X
ejpam-2346	288	2	4	4	NUM
ejpam-2346	288	3	]	]	X
ejpam-2346	288	4	lori	lori	PROPN
ejpam-2346	288	5	a	a	DET
ejpam-2346	288	6	freitag	freitag	NOUN
ejpam-2346	288	7	and	and	CCONJ
ejpam-2346	288	8	patrick	patrick	PROPN
ejpam-2346	288	9	m	m	PROPN
ejpam-2346	288	10	knupp	knupp	PROPN
ejpam-2346	288	11	.	.	PUNCT
ejpam-2346	289	1	tetrahedral	tetrahedral	ADJ
ejpam-2346	289	2	mesh	mesh	NOUN
ejpam-2346	289	3	improvement	improvement	NOUN
ejpam-2346	289	4	via	via	ADP
ejpam-2346	289	5	optimization	optimization	NOUN
ejpam-2346	289	6	of	of	ADP
ejpam-2346	289	7	the	the	DET
ejpam-2346	289	8	element	element	NOUN
ejpam-2346	289	9	condition	condition	NOUN
ejpam-2346	289	10	number	number	NOUN
ejpam-2346	289	11	.	.	PUNCT
ejpam-2346	290	1	international	international	ADJ
ejpam-2346	290	2	journal	journal	PROPN
ejpam-2346	290	3	for	for	ADP
ejpam-2346	290	4	numerical	numerical	ADJ
ejpam-2346	290	5	methods	method	NOUN
ejpam-2346	290	6	in	in	ADP
ejpam-2346	290	7	engineering	engineering	NOUN
ejpam-2346	290	8	,	,	PUNCT
ejpam-2346	290	9	53(6):1377–1391	53(6):1377–1391	NUM
ejpam-2346	290	10	,	,	PUNCT
ejpam-2346	290	11	2002	2002	NUM
ejpam-2346	290	12	.	.	PUNCT
ejpam-2346	291	1	[	[	X
ejpam-2346	291	2	5	5	NUM
ejpam-2346	291	3	]	]	X
ejpam-2346	291	4	lori	lori	PROPN
ejpam-2346	291	5	a	a	DET
ejpam-2346	291	6	freitag	freitag	NOUN
ejpam-2346	291	7	,	,	PUNCT
ejpam-2346	291	8	paul	paul	PROPN
ejpam-2346	291	9	plassmann	plassmann	PROPN
ejpam-2346	291	10	,	,	PUNCT
ejpam-2346	291	11	et	et	PROPN
ejpam-2346	291	12	al	al	PROPN
ejpam-2346	291	13	.	.	PROPN
ejpam-2346	292	1	local	local	ADJ
ejpam-2346	292	2	optimization	optimization	NOUN
ejpam-2346	292	3	-	-	PUNCT
ejpam-2346	292	4	based	base	VERB
ejpam-2346	292	5	simplicial	simplicial	ADJ
ejpam-2346	292	6	mesh	mesh	NOUN
ejpam-2346	292	7	untangling	untangling	NOUN
ejpam-2346	292	8	and	and	CCONJ
ejpam-2346	292	9	improvement	improvement	NOUN
ejpam-2346	292	10	.	.	PUNCT
ejpam-2346	293	1	international	international	ADJ
ejpam-2346	293	2	journal	journal	PROPN
ejpam-2346	293	3	for	for	ADP
ejpam-2346	293	4	numerical	numerical	ADJ
ejpam-2346	293	5	methods	method	NOUN
ejpam-2346	293	6	in	in	ADP
ejpam-2346	293	7	engineering	engineering	NOUN
ejpam-2346	293	8	,	,	PUNCT
ejpam-2346	293	9	49(1):109–125	49(1):109–125	PROPN
ejpam-2346	293	10	,	,	PUNCT
ejpam-2346	293	11	2000	2000	NUM
ejpam-2346	293	12	.	.	PUNCT
ejpam-2346	294	1	[	[	X
ejpam-2346	294	2	6	6	NUM
ejpam-2346	294	3	]	]	PUNCT
ejpam-2346	294	4	patrick	patrick	PROPN
ejpam-2346	294	5	knupp	knupp	PROPN
ejpam-2346	294	6	.	.	PUNCT
ejpam-2346	295	1	remarks	remark	NOUN
ejpam-2346	295	2	on	on	ADP
ejpam-2346	295	3	mesh	mesh	NOUN
ejpam-2346	295	4	quality	quality	NOUN
ejpam-2346	295	5	.	.	PUNCT
ejpam-2346	296	1	technical	technical	ADJ
ejpam-2346	296	2	report	report	PROPN
ejpam-2346	296	3	,	,	PUNCT
ejpam-2346	296	4	sandia	sandia	PROPN
ejpam-2346	296	5	national	national	ADJ
ejpam-2346	296	6	laboratories	laboratory	NOUN
ejpam-2346	296	7	(	(	PUNCT
ejpam-2346	296	8	snl	snl	NOUN
ejpam-2346	296	9	-	-	PUNCT
ejpam-2346	296	10	nm	nm	NOUN
ejpam-2346	296	11	)	)	PUNCT
ejpam-2346	296	12	,	,	PUNCT
ejpam-2346	296	13	albuquerque	albuquerque	NOUN
ejpam-2346	296	14	,	,	PUNCT
ejpam-2346	296	15	nm	nm	PROPN
ejpam-2346	296	16	(	(	PUNCT
ejpam-2346	296	17	united	united	PROPN
ejpam-2346	296	18	states	states	PROPN
ejpam-2346	296	19	)	)	PUNCT
ejpam-2346	296	20	,	,	PUNCT
ejpam-2346	296	21	2007	2007	NUM
ejpam-2346	296	22	.	.	PUNCT
ejpam-2346	297	1	[	[	X
ejpam-2346	297	2	7	7	X
ejpam-2346	297	3	]	]	X
ejpam-2346	297	4	patrick	patrick	PROPN
ejpam-2346	297	5	m	m	PROPN
ejpam-2346	297	6	knupp	knupp	PROPN
ejpam-2346	297	7	.	.	PUNCT
ejpam-2346	298	1	algebraic	algebraic	ADJ
ejpam-2346	298	2	mesh	mesh	NOUN
ejpam-2346	298	3	quality	quality	NOUN
ejpam-2346	298	4	metrics	metric	NOUN
ejpam-2346	298	5	.	.	PUNCT
ejpam-2346	299	1	siam	siam	PROPN
ejpam-2346	299	2	journal	journal	PROPN
ejpam-2346	299	3	on	on	ADP
ejpam-2346	299	4	scientific	scientific	ADJ
ejpam-2346	299	5	computing	computing	NOUN
ejpam-2346	299	6	,	,	PUNCT
ejpam-2346	299	7	23(1):193–218	23(1):193–218	PROPN
ejpam-2346	299	8	,	,	PUNCT
ejpam-2346	299	9	2001	2001	NUM
ejpam-2346	299	10	.	.	PUNCT
ejpam-2346	300	1	[	[	X
ejpam-2346	300	2	8	8	NUM
ejpam-2346	300	3	]	]	X
ejpam-2346	300	4	buddhadev	buddhadev	NOUN
ejpam-2346	300	5	pal	pal	NOUN
ejpam-2346	300	6	and	and	CCONJ
ejpam-2346	300	7	arindam	arindam	PROPN
ejpam-2346	300	8	bhattacharyya	bhattacharyya	PROPN
ejpam-2346	300	9	.	.	PUNCT
ejpam-2346	300	10	regularization	regularization	NOUN
ejpam-2346	300	11	and	and	CCONJ
ejpam-2346	300	12	energy	energy	NOUN
ejpam-2346	300	13	estimation	estimation	NOUN
ejpam-2346	300	14	of	of	ADP
ejpam-2346	300	15	pentahedra	pentahedron	NOUN
ejpam-2346	300	16	(	(	PUNCT
ejpam-2346	300	17	pyramids	pyramid	NOUN
ejpam-2346	300	18	)	)	PUNCT
ejpam-2346	300	19	using	use	VERB
ejpam-2346	300	20	geometric	geometric	ADJ
ejpam-2346	300	21	element	element	NOUN
ejpam-2346	300	22	transformation	transformation	NOUN
ejpam-2346	300	23	method	method	NOUN
ejpam-2346	300	24	.	.	PUNCT
ejpam-2346	301	1	mathematical	mathematical	ADJ
ejpam-2346	301	2	combinatorics	combinatoric	NOUN
ejpam-2346	301	3	,	,	PUNCT
ejpam-2346	301	4	1:67–79	1:67–79	ADV
ejpam-2346	301	5	,	,	PUNCT
ejpam-2346	301	6	2014	2014	NUM
ejpam-2346	301	7	.	.	PUNCT
ejpam-2346	302	1	[	[	X
ejpam-2346	302	2	9	9	NUM
ejpam-2346	302	3	]	]	X
ejpam-2346	302	4	jonathan	jonathan	PROPN
ejpam-2346	302	5	shewchuk	shewchuk	PROPN
ejpam-2346	302	6	.	.	PUNCT
ejpam-2346	303	1	what	what	PRON
ejpam-2346	303	2	is	be	AUX
ejpam-2346	303	3	a	a	DET
ejpam-2346	303	4	good	good	ADJ
ejpam-2346	303	5	linear	linear	ADJ
ejpam-2346	303	6	finite	finite	NOUN
ejpam-2346	303	7	element	element	NOUN
ejpam-2346	303	8	?	?	PUNCT
ejpam-2346	304	1	interpolation	interpolation	NOUN
ejpam-2346	304	2	,	,	PUNCT
ejpam-2346	304	3	conditioning	conditioning	NOUN
ejpam-2346	304	4	,	,	PUNCT
ejpam-2346	304	5	anisotropy	anisotropy	NOUN
ejpam-2346	304	6	,	,	PUNCT
ejpam-2346	304	7	and	and	CCONJ
ejpam-2346	304	8	quality	quality	NOUN
ejpam-2346	304	9	measures	measure	NOUN
ejpam-2346	304	10	(	(	PUNCT
ejpam-2346	304	11	preprint	preprint	NOUN
ejpam-2346	304	12	)	)	PUNCT
ejpam-2346	304	13	.	.	PUNCT
ejpam-2346	305	1	university	university	PROPN
ejpam-2346	305	2	of	of	ADP
ejpam-2346	305	3	california	california	PROPN
ejpam-2346	305	4	at	at	ADP
ejpam-2346	305	5	berkeley	berkeley	PROPN
ejpam-2346	305	6	,	,	PUNCT
ejpam-2346	305	7	73	73	NUM
ejpam-2346	305	8	,	,	PUNCT
ejpam-2346	305	9	2002	2002	NUM
ejpam-2346	305	10	.	.	PUNCT
ejpam-2346	306	1	[	[	X
ejpam-2346	306	2	10	10	NUM
ejpam-2346	306	3	]	]	PUNCT
ejpam-2346	306	4	evan	evan	NOUN
ejpam-2346	306	5	vanderzee	vanderzee	PROPN
ejpam-2346	306	6	,	,	PUNCT
ejpam-2346	306	7	anil	anil	PROPN
ejpam-2346	306	8	n	n	PROPN
ejpam-2346	306	9	hirani	hirani	PROPN
ejpam-2346	306	10	,	,	PUNCT
ejpam-2346	306	11	damrong	damrong	ADJ
ejpam-2346	306	12	guoy	guoy	NOUN
ejpam-2346	306	13	,	,	PUNCT
ejpam-2346	306	14	and	and	CCONJ
ejpam-2346	306	15	edgar	edgar	PROPN
ejpam-2346	306	16	a	a	DET
ejpam-2346	306	17	ramos	ramos	PROPN
ejpam-2346	306	18	.	.	PUNCT
ejpam-2346	307	1	well	well	ADV
ejpam-2346	307	2	-	-	PUNCT
ejpam-2346	307	3	centered	center	VERB
ejpam-2346	307	4	triangulation	triangulation	NOUN
ejpam-2346	307	5	.	.	PUNCT
ejpam-2346	308	1	siam	siam	PROPN
ejpam-2346	308	2	journal	journal	PROPN
ejpam-2346	308	3	on	on	ADP
ejpam-2346	308	4	scientific	scientific	ADJ
ejpam-2346	308	5	computing	computing	NOUN
ejpam-2346	308	6	,	,	PUNCT
ejpam-2346	308	7	31(6):4497–4523	31(6):4497–4523	NUM
ejpam-2346	308	8	,	,	PUNCT
ejpam-2346	308	9	2010	2010	NUM
ejpam-2346	308	10	.	.	PUNCT
ejpam-2346	309	1	[	[	X
ejpam-2346	309	2	11	11	NUM
ejpam-2346	309	3	]	]	X
ejpam-2346	309	4	dimitris	dimitris	PROPN
ejpam-2346	309	5	vartziotis	vartziotis	PROPN
ejpam-2346	309	6	,	,	PUNCT
ejpam-2346	309	7	theodoros	theodoros	NOUN
ejpam-2346	309	8	athanasiadis	athanasiadi	NOUN
ejpam-2346	309	9	,	,	PUNCT
ejpam-2346	309	10	iraklis	iraklis	PROPN
ejpam-2346	309	11	goudas	goudas	PROPN
ejpam-2346	309	12	,	,	PUNCT
ejpam-2346	309	13	and	and	CCONJ
ejpam-2346	309	14	joachim	joachim	PROPN
ejpam-2346	309	15	wipper	wipper	PROPN
ejpam-2346	309	16	.	.	PUNCT
ejpam-2346	310	1	mesh	mesh	NOUN
ejpam-2346	310	2	smoothing	smoothing	NOUN
ejpam-2346	310	3	using	use	VERB
ejpam-2346	310	4	the	the	DET
ejpam-2346	310	5	geometric	geometric	ADJ
ejpam-2346	310	6	element	element	NOUN
ejpam-2346	310	7	transformation	transformation	NOUN
ejpam-2346	310	8	method	method	NOUN
ejpam-2346	310	9	.	.	PUNCT
ejpam-2346	311	1	computer	computer	NOUN
ejpam-2346	311	2	methods	method	NOUN
ejpam-2346	311	3	in	in	ADP
ejpam-2346	311	4	applied	applied	ADJ
ejpam-2346	311	5	mechanics	mechanic	NOUN
ejpam-2346	311	6	and	and	CCONJ
ejpam-2346	311	7	engineering	engineering	NOUN
ejpam-2346	311	8	,	,	PUNCT
ejpam-2346	311	9	197(45):3760–3767	197(45):3760–3767	NUM
ejpam-2346	311	10	,	,	PUNCT
ejpam-2346	311	11	2008	2008	NUM
ejpam-2346	311	12	.	.	PUNCT
ejpam-2346	312	1	[	[	X
ejpam-2346	312	2	12	12	NUM
ejpam-2346	312	3	]	]	X
ejpam-2346	312	4	dimitris	dimitris	PROPN
ejpam-2346	312	5	vartziotis	vartziotis	PROPN
ejpam-2346	312	6	and	and	CCONJ
ejpam-2346	312	7	joachim	joachim	PROPN
ejpam-2346	312	8	wipper	wipper	PROPN
ejpam-2346	312	9	.	.	PUNCT
ejpam-2346	313	1	classification	classification	NOUN
ejpam-2346	313	2	of	of	ADP
ejpam-2346	313	3	symmetry	symmetry	NOUN
ejpam-2346	313	4	generating	generating	NOUN
ejpam-2346	313	5	polygontransformations	polygontransformation	NOUN
ejpam-2346	313	6	and	and	CCONJ
ejpam-2346	313	7	geometric	geometric	ADJ
ejpam-2346	313	8	prime	prime	ADJ
ejpam-2346	313	9	algorithms	algorithm	NOUN
ejpam-2346	313	10	.	.	PUNCT
ejpam-2346	314	1	math	math	NOUN
ejpam-2346	314	2	.	.	PUNCT
ejpam-2346	315	1	pannonica	pannonica	PROPN
ejpam-2346	315	2	,	,	PUNCT
ejpam-2346	315	3	20(2):167	20(2):167	NUM
ejpam-2346	315	4	–	–	PUNCT
ejpam-2346	315	5	187	187	NUM
ejpam-2346	315	6	,	,	PUNCT
ejpam-2346	315	7	2009	2009	NUM
ejpam-2346	315	8	.	.	PUNCT
ejpam-2346	316	1	[	[	X
ejpam-2346	316	2	13	13	NUM
ejpam-2346	316	3	]	]	X
ejpam-2346	316	4	dimitris	dimitris	PROPN
ejpam-2346	316	5	vartziotis	vartziotis	PROPN
ejpam-2346	316	6	and	and	CCONJ
ejpam-2346	316	7	joachim	joachim	PROPN
ejpam-2346	316	8	wipper	wipper	PROPN
ejpam-2346	316	9	.	.	PUNCT
ejpam-2346	317	1	the	the	DET
ejpam-2346	317	2	geometric	geometric	ADJ
ejpam-2346	317	3	element	element	NOUN
ejpam-2346	317	4	transformation	transformation	NOUN
ejpam-2346	317	5	method	method	NOUN
ejpam-2346	317	6	for	for	ADP
ejpam-2346	317	7	mixed	mixed	ADJ
ejpam-2346	317	8	mesh	mesh	NOUN
ejpam-2346	317	9	smoothing	smoothing	NOUN
ejpam-2346	317	10	.	.	PUNCT
ejpam-2346	318	1	engineering	engineer	VERB
ejpam-2346	318	2	with	with	ADP
ejpam-2346	318	3	computers	computer	NOUN
ejpam-2346	318	4	,	,	PUNCT
ejpam-2346	318	5	25(3):287–301	25(3):287–301	PROPN
ejpam-2346	318	6	,	,	PUNCT
ejpam-2346	318	7	2009	2009	NUM
ejpam-2346	318	8	.	.	PUNCT
ejpam-2346	319	1	[	[	X
ejpam-2346	319	2	14	14	NUM
ejpam-2346	319	3	]	]	X
ejpam-2346	319	4	dimitris	dimitris	PROPN
ejpam-2346	319	5	vartziotis	vartziotis	PROPN
ejpam-2346	319	6	and	and	CCONJ
ejpam-2346	319	7	joachim	joachim	PROPN
ejpam-2346	319	8	wipper	wipper	PROPN
ejpam-2346	319	9	.	.	PUNCT
ejpam-2346	320	1	characteristic	characteristic	ADJ
ejpam-2346	320	2	parameter	parameter	NOUN
ejpam-2346	320	3	sets	set	NOUN
ejpam-2346	320	4	and	and	CCONJ
ejpam-2346	320	5	limits	limit	NOUN
ejpam-2346	320	6	of	of	ADP
ejpam-2346	320	7	circulant	circulant	ADJ
ejpam-2346	320	8	hermitian	hermitian	ADJ
ejpam-2346	320	9	polygon	polygon	NOUN
ejpam-2346	320	10	transformations	transformation	NOUN
ejpam-2346	320	11	.	.	PUNCT
ejpam-2346	321	1	linear	linear	ADJ
ejpam-2346	321	2	algebra	algebra	NOUN
ejpam-2346	321	3	and	and	CCONJ
ejpam-2346	321	4	its	its	PRON
ejpam-2346	321	5	applications	application	NOUN
ejpam-2346	321	6	,	,	PUNCT
ejpam-2346	321	7	433(5):945–955	433(5):945–955	NUM
ejpam-2346	321	8	,	,	PUNCT
ejpam-2346	321	9	2010	2010	NUM
ejpam-2346	321	10	.	.	PUNCT
ejpam-2346	322	1	references	reference	NOUN
ejpam-2346	322	2	330	330	NUM
ejpam-2346	322	3	[	[	SYM
ejpam-2346	322	4	15	15	NUM
ejpam-2346	322	5	]	]	X
ejpam-2346	322	6	dimitris	dimitris	PROPN
ejpam-2346	322	7	vartziotis	vartziotis	PROPN
ejpam-2346	322	8	and	and	CCONJ
ejpam-2346	322	9	joachim	joachim	PROPN
ejpam-2346	322	10	wipper	wipper	PROPN
ejpam-2346	322	11	.	.	PUNCT
ejpam-2346	323	1	a	a	DET
ejpam-2346	323	2	dual	dual	ADJ
ejpam-2346	323	3	element	element	NOUN
ejpam-2346	323	4	based	base	VERB
ejpam-2346	323	5	geometric	geometric	ADJ
ejpam-2346	323	6	element	element	NOUN
ejpam-2346	323	7	transformation	transformation	NOUN
ejpam-2346	323	8	method	method	NOUN
ejpam-2346	323	9	for	for	ADP
ejpam-2346	323	10	all	all	ADV
ejpam-2346	323	11	-	-	PUNCT
ejpam-2346	323	12	hexahedral	hexahedral	ADJ
ejpam-2346	323	13	mesh	mesh	NOUN
ejpam-2346	323	14	smoothing	smoothing	NOUN
ejpam-2346	323	15	.	.	PUNCT
ejpam-2346	324	1	computer	computer	NOUN
ejpam-2346	324	2	methods	method	NOUN
ejpam-2346	324	3	in	in	ADP
ejpam-2346	324	4	applied	applied	ADJ
ejpam-2346	324	5	mechanics	mechanic	NOUN
ejpam-2346	324	6	and	and	CCONJ
ejpam-2346	324	7	engineering	engineering	NOUN
ejpam-2346	324	8	,	,	PUNCT
ejpam-2346	324	9	200(9):1186–1203	200(9):1186–1203	NOUN
ejpam-2346	324	10	,	,	PUNCT
ejpam-2346	324	11	2011	2011	NUM
ejpam-2346	324	12	.	.	PUNCT
ejpam-2346	325	1	[	[	X
ejpam-2346	325	2	16	16	NUM
ejpam-2346	325	3	]	]	X
ejpam-2346	325	4	dimitris	dimitris	PROPN
ejpam-2346	325	5	vartziotis	vartziotis	PROPN
ejpam-2346	325	6	,	,	PUNCT
ejpam-2346	325	7	joachim	joachim	PROPN
ejpam-2346	325	8	wipper	wipper	PROPN
ejpam-2346	325	9	,	,	PUNCT
ejpam-2346	325	10	and	and	CCONJ
ejpam-2346	325	11	bernd	bernd	PROPN
ejpam-2346	325	12	schwald	schwald	NOUN
ejpam-2346	325	13	.	.	PUNCT
ejpam-2346	326	1	the	the	DET
ejpam-2346	326	2	geometric	geometric	ADJ
ejpam-2346	326	3	element	element	NOUN
ejpam-2346	326	4	transformation	transformation	NOUN
ejpam-2346	326	5	method	method	NOUN
ejpam-2346	326	6	for	for	ADP
ejpam-2346	326	7	tetrahedral	tetrahedral	ADJ
ejpam-2346	326	8	mesh	mesh	NOUN
ejpam-2346	326	9	smoothing	smoothing	NOUN
ejpam-2346	326	10	.	.	PUNCT
ejpam-2346	327	1	computer	computer	NOUN
ejpam-2346	327	2	methods	method	NOUN
ejpam-2346	327	3	in	in	ADP
ejpam-2346	327	4	applied	applied	ADJ
ejpam-2346	327	5	mechanics	mechanic	NOUN
ejpam-2346	327	6	and	and	CCONJ
ejpam-2346	327	7	engineering	engineering	NOUN
ejpam-2346	327	8	,	,	PUNCT
ejpam-2346	327	9	199(1):169–182	199(1):169–182	NUM
ejpam-2346	327	10	,	,	PUNCT
ejpam-2346	327	11	2009	2009	NUM
ejpam-2346	327	12	.	.	PUNCT