38 Color Culture and Science Journal Vol. 14 (2) DOI: 10.23738/CCSJ.140205 

Digital applications to train color ordering in 

three dimensions for architects and 

designers 
Juan Serra

1
, Javier Cortina Maruenda

1
, Ana Torres Barchino

1
, Jorge Llopis

1
  

1 
Grupo de Investigación de Color en Arquitectura, Instituto de Restauración del Patrimonio, 

Universitat Politècnica de València; juanserra@ega.upv.es, javier.cortinamaruenda@ega.upv.es, 
atorresb@ega.upv.es, jllopis@ega.upv.es,  

Corresponding author: ; Juan Serra (juanserra@ega.upv.es) 

 

 

ABSTRACT 

 
Gamification is one of the main motivation and learning strategies of current generations. On the other hand, 

the study of color from the creation of the Bauhaus through the exercises developed by Joseph Albers has 

always had an undeniable component of experimentation. Motivated by this double idea, from the Color in 

Architecture Research Group we have studied the use of games in the training of architects for color 

discrimination. Among all the games aimed at training colour discrimination, puzzles are probably the most 

widespread. It is noteworthy that almost all of them use flat geometries, ignoring the fact that colors have 

three perceptual variables, and the main colour notation systems render 3D solids. It is enough to name 

Munsell or NCS color solids to recognise this spatial variable. So space will be a variable to be taken into 

account in our study, becoming one of the characteristics more intimately related to the profession of 

architecture. Maybe one of the most important skills that an architect must have is the mastery of spatial 

vision. In this way, the studio tries to combine gamification, training in colour discrimination and 3D 

management for architects. 

 

KEYWORDS architecture, geometry, color order system, gamification, puzzle, app 

 
RECEIVED 30/03/2022; REVISED 08/08/2022; ACCEPTED 11/10/2022 

 

 

 
  

mailto:juanserra@ega.upv.es
mailto:jllopis@ega.upv.es
mailto:juanserra@ega.upv.es


Digital applications to train color ordering in three dimensions for architects and designers 

39 Color Culture and Science Journal Vol. 14 (2) DOI: 10.23738/CCSJ.140205 

1. Introduction 

In the acquisition of skills to work with the color for an 

architect or an interior designer, it is important to train 

the visual discrimination of colors and to gain the 

sensitivity to display different colors in order. Both 

learnings are on the roots of the different color curricula 

in the architecture schools since the beginning of the 

XXth Century and are considered essential knowledge.  

Gamification demonstrates to be a good way of 

involving students in the acquisition of these skills that 

not only need a rational understanding of color theory, 

but also need to be naturally integrated as an 

instinctive skill, something that happens after a 

dedicated training. Among all the types of games used 

for learning, digital color puzzles are good alternatives 

to train these abilities. But it is noteworthy that, despite 

having color three perceptual variables, most of the 

available color puzzles keep working with just two 

dimensions of color. For this reason, the app 

ColorDoku 3d, aims to ease the understanding that 

color has three perceptual variables, and to train the 

visual discrimination of these variables. The app also 

gives the opportunity to get familiar with interesting and 

difficult to understand polyhedron.  

 

2. The teaching of color order systems in 

architecture curricula  

The description of color as a visual phenomenon with 

three perceptual variables, hue, value and saturation, 

allowed the proposition of different three-dimensional 

models since the beginning of the XIXth century, with 

different shapes depending on the arrangement of the 

fundamental colors and specific nomenclatures for the 

variables. 

The time for using linear systems or two-dimensional 

diagrams such as the ones developed by Goethe in his 

Theory of Colors (1810) or by Neewton in his chromatic 

circle (1704) is far behind us. At present, among all the 

three-dimensional models, two are the most popular for 

art and design: The Munsell Color System, and the 

Natural Color System (NCS) [1]. At the Munsell Color 

System, colors are identified by three parameters, hue, 

value and chroma. With this data, you can obtain the 

coordinates of any color in the Munsell solid. Color 

Solid has an irregular three dimensional shape as a 

consequence of this system based in visual color 

perception. On the other hand, the structure of the NCS 

color solid is based in three pairs of opponent colors: 

white-black, green-red and yellow-blue. Its geometry is 

a regular symmetric double cone (Nemcsis and 

Caivano 2015) (Figure 1). 

 

Figure 1: The NCS Natural Color System (The Natural 

Colour System is the copyright and trademark property of 

NCS Colour AB) (1979) by Anders Hård and Lars Sivik.  

 
The ability to discriminate colors and organize them in the 

right order is a worth training for architects and artists, as 

it improves their sensitivity and expands their color 

abilities. For these reasons, almost all the modern color 

curricula for architects included the study of color circles 

and other similar organizations of colors with a certain 

logic (Hirschler et al. 2018). This was also the case of the 

basic courses at the Bauhaus Dessau and the 

Hochschule für Gestaltung Ulm, with important 

academics such as Albers, Itten, Maldonado, etc. Later 

on, Annie and Joseph Albers kept training students in 

color skills with interesting experiences at the Black 

Mountain College inNorth Carolina (Tóth, Molnár and 

Kárpáti 2021, Campos and Moya 2021).  

In recent years, some of the traditional color exercises 

shifted into a digital version, as it happened with the 

perennial Interaction of Color by Joseph Albers (Franco 

Taboada 2015). This book has been developed as an 

iPad application, surpassing the original format in 

content. This App published by Yale University Press has 

been widely awarded and recognized (Figure 2). 

Nevertheless, some of these traditional exercises need 

personal involvement, are time-consuming, and not 

always are easy for generations of students and 

professionals that are becoming more impatient and less 

persistent. When waiting has become an intolerable 

matter, the impatience syndrome appears. This 

syndrome affects not only the current generation of 

students but seems to extend to future generations 

(Bauman 2015). 

At the same time, in a completely digitalized society, 

gamification gives an opportunity to improve the color 

skills, and the pleasure of organizing colors in order is on 

the roots of a big number of digital games: Blendoku 

(Lonely Few 2015), Chroma Rush (Lonely Few 2017), I 

Love hue (Zut 2017), Blendoku 2 (Lonely Few 2019), 

Chromatic: Color Puzzles (2019), Tinge: A Color Game 

(Suwao LLC 2019), Chroma (Noisy Duck 2021), I Love 

Hue Too (2021), etc. Gamification is the use of non-



Digital applications to train color ordering in three dimensions for architects and designers 

40 Color Culture and Science Journal Vol. 14 (2) DOI: 10.23738/CCSJ.140205 

game-in-context game mechanics, elements, and design 

techniques to engage users and solve problems 

(Zichermann & Cunningham, 2011; Werbach & Hunter, 

2012). 

In general, this type of game provides a series of colours 

to be included in an incomplete two-dimensional pattern. 

The patterns used in these games are usually simple 

rows and columns of colour gradations, like in the game 

Blendoku. In this case the difficulty level increases with 

the inclusion of more pieces to place in the puzzle, and 

having a smaller chromatic variation. In the case of I Love 

Hue Too, the puzzles are based on complex mosaics and 

the level difficulty level increase, as in the other games, 

with the number of colors to fill, and the geometry 

complexity. 

As indicated, all these apps have a two-dimensional 

interface and forget that color is a three-dimensional 

perceptual phenomenon. Nevertheless, the spatial 

representation of colors with their three perceptual 

variables results in some non-regular solids like 

spheroids, cylinders, double cones and many other 

geometries depending on the color system used. Being 

most of them not regular bodies, the colour discrimination 

learning can benefit from using three dimensional solids, 

as well as the understanding of complex regular bodies 

can be boosted by playing with the three variables of 

colors. For all these reasons, a puzzle in three 

dimensions to order colors onto regular bodies might be 

beneficial for architecture students.  

 

  

            
 
 
Figure 2: Interaction of Color, is a digital version of the traditional exercises of J. Albers in a digital way. 
 
 

3. The teaching of regular bodies in architecture 

curricula  

To have a robust spatial imagination is an essential skill 

for an architect, and so it is the understanding and 

manipulation of three-dimensional objects. If we review 

the European history of architecture, this ability has 

traditionally been cultivated with the study of regular 

polyhedra with complex geometries that we find since 

the most important treatises of geometry belonging to 

the Renaissance period. Even today we can find the 

study, drawing and analysis of these geometries forming 

a fundamental part of the theoretical “corpus” of Graphic 

Expression subjects. Books as Beyond the Cube: The 

Architecture of Space Frames and Polyhedra by Jean-

François Gabriel (1997), continue to maintain the 

interest and relationship between polyhedrons and 

architecture. Works of Louis Kahn (1910-1974), 

Buckminster Fuller (1895-1983) and Philip Johnson 

(1906-2005), among other, are a clear example of this 

idea. 

One of the fundamental and first books that study and 

analyse this subject it’s the De Divina Proportione 

(1509) written by the mathematician Luca Pacioli and 

illustrated by Leonardo da Vinci. This mathematical 

treatise praises mathematics as the basis of science 

and architecture. The book contains a small section on 

architecture, but undoubtedly one of its main assets is 

the study of regular polyhedra. These polyhedra are 

represented using the most cutting edged graphic 

resources of that period to help in the understanding of 



Digital applications to train color ordering in three dimensions for architects and designers 

41 Color Culture and Science Journal Vol. 14 (2) DOI: 10.23738/CCSJ.140205 

its geometries. By alternating the drawing of solid 

geometries and solids represented in wire frame in more 

than 60 draws, it was possible an easy distinction 

between front and back edges, (Figure 3a).  

 

 

Figure 3: a) Representation of an icosahedron, 

Ycocedron Planus Vacuus, by Leonardo da Vinci for De 

Divina Proportione (Luca Pacioli, 1509); b) Oliver Byrne, 

The First Six Book of the Elements of Euclid, London, 

1847. Book I Prop. XXXVII "Triangles on the same base 

and between the same parallels are equal".  

 

In the XIXth century, the color was also used as a 

graphic resource for a better understanding of 

geometry. This is the case of the founding text of 

geometry The Elements (Στοιχεῖα) written by Euclides 

(325-265 bC), that was reedited by Oliver Byrne in 1847 

with graphical codes of colors replacing the original text. 

As the same Byrne wrote in his foreword “we do not 

introduce colour for the purpose of entertainment, or to 

amuse by certain combinatios of tint and form, but to 

assist the mind in its researches after truth, to increase 

the facilities of instruction, and to diffuse permanent 

knowledge” (Byrne 1847, quoted in Higón-Calvet 2013). 

The combination of colors and geometry resulted in a 

very beautiful and easy to understand publication 

(Figure 3b). Nowadays, as we have already explained, 

as it has happened with other colour-related knowledge, 

the videos and animated graphics with continuous 

movement seem to be the most adequate means of 

expression to explain and understand geometries, with 

interesting websites explaining geometric concepts in 

three dimensions. [2] 

 

4. Description of the app ColorDoku 3d  

To merge the knowledge about regular bodies and color 

understanding, a group of academics and students 

developed a digital app called ColorDoku 3d, that is 

available for free at the web page of the Color Research 

Group in Architecture UPV. [3] By the moment, it 

contains four regular solids with triangular faces: 

icosahedron (20 triangular faces), triacysthetrahedron 

(12 triangular faces), tetrahexahedron (24 triangular 

faces) and hexaquisocta-hedron (48 triangular faces) 

(Figure 4).  

The icosahedron is a polyhedron that belongs to the 

Platonic solids, and has been widely represented and 

used since antiquity. Platonic solids are those that have 

all faces equal and are a regular polygon. There are 

only five, for this app we choose the only one that 

represented a certain complexity for the game.  

The other three polyhedra belong to the family of 

Catalan solids. These polyhedra were published in 1865 

for the first time by the Belgian mathematician Eugène 

Charles Catalan after whom they are named. There are 

only thirteen and are generated with two Archimedes 

solids. So, their faces have irregular polygons but equal 

dihedric angles. This type of polyhedra, besides being 

part of the basic teaching in architecture for the control 

of geometry, has also had practical applications in the 

use of vaults (Mallo 2013). We chose for the puzzle the 

triacysthetrahedron, tetrahexahedron and 

hexaquisoctahedron. These solids have faces with 

triangular bases, so they were more suitable for 

programming.  

The triacysthetrahedron is a truncated tetrahedron, the 

tetrahexahedron is a truncated octahedron and the 

hexaquisoctahedron is a truncated cuboctahedron.  

 

 

 

Figure 4: The four regular bodies implemented in 

ColorDoku 3d: a) icosahedron, b) triacysthetrahedron, c) 

tetrahexahedron and d) hexaquisoctahedron. 



Digital applications to train color ordering in three dimensions for architects and designers 

42 Color Culture and Science Journal Vol. 14 (2) DOI: 10.23738/CCSJ.140205 

 
 
Figure 5: View of the research group's website (GICA). Application login screen. https://grupocolor.webs.upv.es/?page_id=3021 

 

 

Figure 6: Interface of ColorDuku 3d with an uncompleted 

puzzle of an icosahedron.  

 

In the initial screen of the app, users can choose 

between the four aforementioned polyhedra, and set 

different parameters depending on the expected level of 

difficulty for the game, such as the scale of the solid, its 

position inside the color space, and the number of faces 

of the figure that will appear with the colors already set. 

With this information, a color palette is displayed and 

the 3d puzzle is launched. Turning the figure round in 

any direction and increasing its size if needed, users 

can drag and drop the colors provided in the color 

palette into the right faces of the solid to complete the 

3d puzzle.  

The level of difficulty increases with the number of faces 

of the selected solid and with the scale of the selected 

solid. The difficulty is directly proportional to the number 

of faces and inversely proportional to the scale of the 

chosen solid. 

In the screen of the settings, and when the scale of the 

regular body is under 100%, it is possible to place it in 

different positions inside a virtual cube. This cube 

represents the color space HSL (Hue, Saturation, 

lightness), which is an alternative model to RGB, and 

therefore a useful color space for digital displays. When 

the user selects different values between 0% and 100% 

for the three spatial directions X, Y and Z, is placing the 

solid in a different position into the HSL space. The app 

will automatically generate a color palette assigning to 

each triangular face of the solid the color corresponding 

to the barycenter of such a face in the HSL model. 

When the 3d puzzle is launched, the interface is divided 

into two parts (Figure 6). On the left side there is a color 

palette with all the colors of the puzzle in a random 

order, and on the right side the user can rotate and 

scale the solid. Those colors preset have a grey cross 

on the color palette and a black dot on the 

corresponding face to indicate that they are locked. The 

rest of the colors in the color palette can be dragged 

and dropped onto the corresponding faces. With the 



Digital applications to train color ordering in three dimensions for architects and designers 

43 Color Culture and Science Journal Vol. 14 (2) DOI: 10.23738/CCSJ.140205 

help of an eraser, the user can remove a color placed in 

a wrong position that will automatically move back to the 

color palette. When the 3d puzzle is correctly completed 

the indication “puzzle completed” appears. 

We hope that this new app will help to improve at the 

same time the perceptual color discrimination ability 

together with the spatial vision.  

 

5. Results and conclusions  

Durint the 2020/21 course we invited the students 

enrolled in the subject Graphic and Chromatic Design of 

the Master in Architecture of the UPV to train with 

ColorDoku 3d and give their opinion. A total of 18 

students (12 females, 6 males; Mean age= 23) played 

with the app for a couple of days and gave feedback via 

an online questionnaire. Regarding the selection of the 

polyhedra, icosahedron was the most selected (50%), 

followed by tetrahexahedron (27.8%), 

hexaquisoctahedron (16.7%) and triacysthetra-hedron 

(5.6%), therefore the selection of the polyhedra seemed 

to be rooted in a personal attachment and not in the 

number of faces of the solid or its difficulty. According to 

the answers, 33.3% of the respondents considered the 

random colors combination provided beautiful, 22.2% not 

beautiful and 44.4% indifferent. Considering the difficulty 

of the 3d puzzle, 44.4% considered it easy, 33.3% 

intermediate and 21.7% difficult or very difficult, with this 

assessment dependent on the puzzle settings of each 

participant. In an informal interview in the classroom, 

students expressed their interest in the app, indicating 

that it was fun and engaging, but also pointing out some 

aspects to improve, particularly related with the interface 

and the general user-friendliness of the app. Students 

seemed to be in favor of having an automatic preset of 

the parameter of the puzzle.  

We conclude that ColorDoku 3d can be a useful tool for 

the education of students in the improvement of their 

perceptual color discrimination ability and spatial vision, 

being a complementary resource to train their color 

abilities out of the classroom via gamification. In the 

future, the app will need some upgrades to make it more 

user-friendly and engaging, considering the information 

provided by a target group of users. In future 

developments, it will be important to have more 

evidences to evaluate the improvement of knowledge of 

solids and colors after training with ColorDuku 3d.  

 

6. Acknowledgements  

We want to acknowledge David de Andrés that belongs 

to the ITACA group, Universitat Politècnica de València 

for and Irene Cebrián Onsurbe and her work in the 

technical development of ColorDoku 3d. 

 

7. Conflict of interest declaration  

The autors declare that they have not actual or potencial 

conflict of interest including financial, personal, or other 

relationships with other people or organizations within 

three years of beginning the submitted work that could 

inappropriately influence, or be perceived to influence, 

their work. 

 

8. Funding source declaration 

All authors declare that the investigation has not been 

supported or paid by any funding sources or research 

grants  

 

9. Authors short biography 

Juan Serra Lluch - PhD architect, full-time professor and 

subdirector of research in the School of Architecture of 

Valencia. Member of the Color Research Group of the 

Heritage Restoration Institute of the Universitat 

Poltècnica de València, with expertise in color in Modern 

and Contemporary architecture. Author of numerous 

papers and the textbook Color for Architects (PAPress, 

2019). 

Javier Cortina Maruenda - PhD architect, full-time 

professor and Member of the Color Research Group of 

the Heritage Restoration Institute of the Universitat 

Poltècnica de València.  

Ana Torres Barchino - Phd in Fine Arts from the 

Universitat Politècnica de València. Professor in the 

Graphic Expression Department in the UPV. Degree in 

Master in Conservation and Restoration of Architectural 

and Urban Heritage by the Polytechnic University of 

Madrid. Her research lines are focused on the analysis of 

colour in architectural heritage and design. 

Jorge Llopis. Phd. Architect and Full Professor at the 

Universitat Politècnica de València in the Graphic 

Expression Department. His research lines are focused 

on the analysis of documentary and cartographic 

information on architectural heritage and on the study of 

new architectural graphic strategies after the arrival of 

digital drawing. 

 

Notes  

[1] There are many other systems for ordering colours in a three-

dimensional space organised by three perceptual variables. Among 



Digital applications to train color ordering in three dimensions for architects and designers 

44 Color Culture and Science Journal Vol. 14 (2) DOI: 10.23738/CCSJ.140205 

them, the Coloroid System developed by Nemecsis between 1962 and 

1980 stands out. This system uses hue as an angular coordinate, 

saturation as a radial coordinate and luminosity as a vertical coordinate. 

[2] http://www.matematicasvisuales.com/index.html 

[3] https://grupocolor.webs.upv.es/ 

 

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