Visualization of Polyhedra tessellation with Virtual Reality (VR) in A-frame
author: Paulo Henrique Siqueira - Universidade Federal do Paraná
contact: paulohscwb@gmail.com
versão em português
Tessellation - part 2
The figures or works that are chosen as tesserae cover or pave the plane or a surface. The result is called tessellation, tiling, paving or mosaic.
Tessellations have been used since ancient times in floors, walls, carpets and other objects.
This work shows the tessellations made on all or some faces of polyhedrons, taking advantage of triangular, square, pentagonal or hexagonal symmetries of the faces of these solids.
On this page, we have some tessellation works by Francine Champagne, Massimo Rana, Alain Nicolas and Barb Widen, inserted into the faces of common polyhedrons, such as the Platonic tetrahedron, cube or icosahedron, as well as rarer polyhedrons, such as the Johnson solids.
3D models
1. Francine Champagne tessellation
description: Francine Champagne tessellation 2019 - Eck Master Lai Tsi from ancient China
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron
2. Francine Champagne tessellation
description: Francine Champagne tessellation 2019 - Eck Master Lai Tsi from ancient China
tessellation type: triangular and quadrilateral
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron
3. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Amphibian
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron
4. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Amphibian
tessellation type: triangular and quadrilateral
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron
5. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Angel queen
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Möbius 10-akis dodecahedron, Escher solid, hexakis tetrahedron, Möbius hexakis icosahedron, octahedron, Möbius deltahedron, Möbius octakis hexahedron, tetrakis hexahedron
6. Barb Widen tessellation
description: Barb Widen tessellation
tessellation type: quadrilateral and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron, deltoidal icositetrahedron, cube, cuboctahedron, triakis octahedron, triakis icosahedron
7. Barb Widen tessellation
description: Barb Widen tessellation
tessellation type: quadrilateral and triangular
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, rhombic triacontahedron, square orthobicupola, stella octangula, triakis tetrahedron
8. Francine Champagne tessellation
description: Francine Champagne tessellation - Prissy Groovy and Cool
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron, deltoidal icositetrahedron, cube, pentakis dodecahedron, triakis octahedron, triakis icosahedron
9. Francine Champagne tessellation
description: Francine Champagne tessellation - Prissy Groovy and Cool
tessellation type: triangular and quadrilateral
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, rhombic triacontahedron, square orthobicupola, stella octangula, triakis tetrahedron
10. Alain Nicolas tessellation
description: Alain Nicolas tessellation - On the beach 3
tessellation type: quadrilateral and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron
11. Alain Nicolas tessellation
description: Alain Nicolas tessellation - On the beach 3
tessellation type: quadrilateral and triangular
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron
12. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Mosaic of earth, air and water
tessellation type: quadrilateral and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron, deltoidal icositetrahedron, cube, cuboctahedron, triakis octahedron, triakis icosahedron
13. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Mosaic of earth, air and water
tessellation type: quadrilateral and triangular
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, rhombic triacontahedron, square orthobicupola, triakis tetrahedron
14. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Air, earth & sea 1
tessellation type: quadrilateral and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron
15. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Air, earth & sea 1
tessellation type: quadrilateral and triangular
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron
16. Francine Champagne tessellation
description: Francine Champagne tessellation - Three Dogs Searching for the Crumb
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron, deltoidal icositetrahedron, cube, pentakis dodecahedron, triakis octahedron, triakis icosahedron
17. Francine Champagne tessellation
description: Francine Champagne tessellation - Three Dogs Searching for the Crumb
tessellation type: triangular and quadrilateral
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, rhombic triacontahedron, square orthobicupola, stella octangula, triakis tetrahedron
18. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Cherubs & demons
tessellation type: quadrilateral and triangular
polyhedra: Möbius hexakis octahedron, Möbius 10-akis dodecahedron, Escher solid, hexakis tetrahedron, Möbius hexakis icosahedron, octahedron, Möbius deltahedron, Möbius octakis hexahedron, tetrakis hexahedron
19. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Three chinese
tessellation type: quadrilateral and triangular
polyhedra: Möbius hexakis octahedron, Möbius 10-akis dodecahedron, Escher solid, hexakis tetrahedron, Möbius hexakis icosahedron, octahedron, Möbius deltahedron, Möbius octakis hexahedron, tetrakis hexahedron, rhombic dodecahedron
20. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Duck 120º
tessellation type: quadrilateral and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron
21. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Duck 120º
tessellation type: quadrilateral and triangular
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron
22. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Fire queen
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Möbius 10-akis dodecahedron, Escher solid, hexakis tetrahedron, Möbius hexakis icosahedron, octahedron, Möbius deltahedron, Möbius octakis hexahedron, tetrakis hexahedron
23. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Royal fish
tessellation type: quadrilateral and triangular
polyhedra: Möbius hexakis octahedron, Möbius 10-akis dodecahedron, Escher solid, hexakis tetrahedron, Möbius hexakis icosahedron, octahedron, Möbius deltahedron, Möbius octakis hexahedron, tetrakis hexahedron
24. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Heartbug
tessellation type: quadrilateral and triangular
polyhedra: Möbius hexakis octahedron, Möbius 10-akis dodecahedron, Escher solid, hexakis tetrahedron, Möbius hexakis icosahedron, octahedron, Möbius deltahedron, Möbius octakis hexahedron, tetrakis hexahedron
25. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Li’l dragon
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron
26. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Li’l dragon
tessellation type: triangular and quadrilateral
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron
27. Francine Champagne tessellation
description: Francine Champagne tessellation - Three Rubber Duckies
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron, deltoidal icositetrahedron, cube, pentakis dodecahedron, triakis octahedron, triakis icosahedron
28. Francine Champagne tessellation
description: Francine Champagne tessellation - Three Rubber Duckies
tessellation type: triangular and quadrilateral
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, rhombic triacontahedron, square orthobicupola, stella octangula, triakis tetrahedron
29. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Air, earth & sea 2
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron
30. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Air, earth & sea 2
tessellation type: triangular and quadrilateral
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron
31. Alain Nicolas tessellation
description: Alain Nicolas tessellation - 9 lizards noses
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron
32. Alain Nicolas tessellation
description: Alain Nicolas tessellation - 9 lizards noses
tessellation type: triangular and quadrilateral
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron
33. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Monsters
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron, cuboctahedron
34. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Monsters
tessellation type: triangular and quadrilateral
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron
35. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Panda, bat & fish
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron
36. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Panda, bat & fish
tessellation type: triangular and quadrilateral
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron
37. Alain Nicolas tessellation
description: Alain Nicolas tessellation - On the beach 2
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron
38. Alain Nicolas tessellation
description: Alain Nicolas tessellation - On the beach 2
tessellation type: triangular and quadrilateral
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron
39. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Squirrel, bird & fish
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron
40. Alain Nicolas tessellation
description: Alain Nicolas tessellation - Squirrel, bird & fish
tessellation type: triangular and quadrilateral
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron
41. Alain Nicolas tessellation
description: Alain Nicolas tessellation - On the beach 1
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Möbius 10-akis dodecahedron, Escher solid, hexakis tetrahedron, Möbius hexakis icosahedron, octahedron, Möbius deltahedron, Möbius octakis hexahedron, tetrakis hexahedron, rhombic dodecahedron
42. Francine Champagne tessellation
description: Work from 2014 - Hummingbird tessellation in symmetry group P4m
tessellation type: triangular
polyhedra: Möbius hexakis octahedron, Möbius 10-akis dodecahedron, Escher solid, hexakis tetrahedron, Möbius hexakis icosahedron, octahedron, Möbius deltahedron, Möbius octakis hexahedron, tetrakis hexahedron
43. Alain Nicolas tessellation
description: Alain Nicolas tessellation - On the beach 3
tessellation type: triangular
polyhedra: Möbius hexakis octahedron, Möbius 10-akis dodecahedron, Escher solid, hexakis tetrahedron, Möbius hexakis icosahedron, octahedron, Möbius deltahedron, Möbius octakis hexahedron, tetrakis hexahedron
44. Massimo Rana tessellation
description: Massimo Rana tessellation
tessellation type: triangular
polyhedra: icosahedron, great icosahedron, Escher solid, hexakis tetrahedron, snub disphenoid, Möbius deltahedron, octahedron, Möbius hexakis octahedron, pentakis dodecahedron
45. Massimo Rana tessellation
description: Massimo Rana tessellation
tessellation type: triangular
polyhedra: Möbius hexakis icosahedron, pentagonal dipyramid, Möbius octakis hexahedron, Möbius 10-akis dodecahedron, stella octangula, tetrahedron, tetrakis hexahedron
Tessellation - part 2: polyhedra tessellation and visualization with Virtual Reality by Paulo Henrique Siqueira is licensed with a license Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International.
How to cite this work:
Siqueira, P.H., "Tessellation - part 2: polyhedra tessellation and visualization with Virtual Reality". Available in: <https://paulohscwb.github.io/tessellation/part2/>, May 2025.
References:
Nicolas, A. “Tessellations: Art most in harmony with the natural order - Method & Galleries” https://en.tessellations-nicolas.com/
Champagne, F. “Tessellations by Francine Champagne” https://tessellations.ca/
Weisstein, Eric W. “Tessellation.” From MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/Tessellation.html
Mohr, R. “Tiled Art” https://tiled.art/en/home
McCooey, D. I. “Visual Polyhedra”. http://dmccooey.com/polyhedra/