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 3
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, Velirina, Goshashka, Misbah Rani and Vladimir Bulatov, 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. Vladimir Bulatov tessellation
description: Vladimir Bulatov tessellation - Circle limit
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, Hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, Deltoidal hexecontahedron, Deltoidal icositetrahedron, Cube, Great Ditrigonal Dodecacronic Hexecontahedron, Truncated Dodecadodecahedron, Great Truncated Icosidodecahedron
2. Vladimir Bulatov tessellation
description: Vladimir Bulatov tessellation - Circle limit
tessellation type: triangular and quadrilateral
polyhedra: Rhombic dodecahedron, Möbius 10-akis dodecahedron, Möbius hexakis icosahedron, Octahedron, Tetrakis hexahedron, Pentagonal dipyramid, Medial Deltoidal Hexecontahedron, Triakis tetrahedron, Triakis Octahedron, Triakis Icosahedron
3. Vladimir Bulatov tessellation
description: Vladimir Bulatov tessellation - Circle limit
tessellation type: triangular and quadrilateral
polyhedra: Great Dirhombicosidodecahedron, Medial Rhombic Triacontahedron, Small Dodecacronic Hexecontahedron, Great Hexacronic Icositetrahedron, Medial Icosacronic Hexecontahedron, Rhombidodecadodecahedron, Stella octangula, Small Icosacronic Hexecontahedron, Great Rhombic Triacontahedron, Great Rhombihexahedron, Great Rhombidodecahedron
4. Francine Champagne tessellation
description: Francine Champagne tessellation - Snowflake
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, Hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, Deltoidal hexecontahedron, Deltoidal icositetrahedron, Cube, Cuboctahedron, Pentagonal dipyramid, Tetrahedron
5. Francine Champagne tessellation
description: Francine Champagne tessellation - Snowflake
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, Icosahedron, Pentakis dodecahedron
6. Mandala tessellation
description: Mandala tessellation
tessellation type: pentagonal
polyhedra: Pentagonal icositetrahedron, Tetartoid, Pentagonal hexecontahedron, Dodecahedron, Great Dodecahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron, Small Ditrigonal Icosidodecahedron, Ditrigonal Dodecadodecahedron, Snub Icosidodecadodecahedron, Great Ditrigonal Dodecicosidodecahedron
7. Mandala tessellation
description: Mandala tessellation
tessellation type: pentagonal
polyhedra: Snub Dodecadodecahedron, Medial Pentagonal Hexecontahedron, Dodecadodecahedron, Great Ditrigonal Icosidodecahedron, Great Icosidodecahedron, Icosidodecadodecahedron, Inverted Snub Dodecadodecahedron, Great Pentagonal Hexecontahedron, Great Inverted Pentagonal Hexecontahedron
8. Misbah Rani tessellation
description: Misbah Rani tessellation
tessellation type: triangular and quadrilateral
polyhedra: Deltoidal hexecontahedron, Rhombic triacontahedron, Cube, Rhombic dodecahedron, Rhombic hexecontahedron, Deltoidal icositetrahedron, Escher solid, Great Dodecacronic Hexecontahedron, Triakis tetrahedron, Triakis Octahedron, Triakis Icosahedron
9. Misbah Rani tessellation
description: Misbah Rani tessellation
tessellation type: triangular and quadrilateral
polyhedra: Great Rhombic Triacontahedron, Hexakis tetrahedron, Medial Deltoidal Hexecontahedron, Medial Icosacronic Hexecontahedron, Medial Rhombic Triacontahedron, Pentagonal dipyramid, Rhombidodecadodecahedron, Small Dodecacronic Hexecontahedron
10. Misbah Rani tessellation
description: Misbah Rani tessellation
tessellation type: quadrilateral and triangular
polyhedra: Great Icosacronic Hexecontahedron, Stella octangula, Truncated Dodecadodecahedron, Great Rhombihexahedron, Small Icosacronic Hexecontahedron, Tetrakis hexahedron, Great Rhombidodecahedron, Great Truncated Icosidodecahedron
11. Star tessellation
description: Star tessellation
tessellation type: pentagonal
polyhedra: Pentagonal icositetrahedron, Tetartoid, Pentagonal hexecontahedron, Dodecahedron, Great Dodecahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron, Small Ditrigonal Icosidodecahedron, Ditrigonal Dodecadodecahedron, Snub Icosidodecadodecahedron, Great Ditrigonal Dodecicosidodecahedron
12. Star tessellation
description: Star tessellation
tessellation type: pentagonal
polyhedra: Snub Dodecadodecahedron, Medial Pentagonal Hexecontahedron, Dodecadodecahedron, Great Ditrigonal Icosidodecahedron, Great Icosidodecahedron, Icosidodecadodecahedron, Inverted Snub Dodecadodecahedron, Great Pentagonal Hexecontahedron, Great Inverted Pentagonal Hexecontahedron
13. Square tessellation
description: Square 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, Pentakis dodecahedron
14. Square tessellation
description: Square 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
15. Square tessellation
description: Square tessellation
tessellation type: quadrilateral and triangular
polyhedra: Pentagonal dipyramid, Tetrahedron, Icosahedron, Great Icosahedron, Great Rhombidodecahedron, Great Truncated Icosidodecahedron, Truncated Dodecadodecahedron, Great Rhombihexahedron, Triakis tetrahedron, Triakis Octahedron, Triakis Icosahedron
16. Goshashka tessellation
description: Goshashka tessellation
tessellation type: pentagonal
polyhedra: Pentagonal icositetrahedron, Tetartoid, Pentagonal hexecontahedron, Dodecahedron, Great Dodecahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron, Small Ditrigonal Icosidodecahedron, Ditrigonal Dodecadodecahedron, Snub Icosidodecadodecahedron, Great Ditrigonal Dodecicosidodecahedron
17. Goshashka tessellation
description: Goshashka tessellation
tessellation type: pentagonal
polyhedra: Snub Dodecadodecahedron, Medial Pentagonal Hexecontahedron, Dodecadodecahedron, Great Ditrigonal Icosidodecahedron, Great Icosidodecahedron, Icosidodecadodecahedron, Inverted Snub Dodecadodecahedron, Great Pentagonal Hexecontahedron, Great Inverted Pentagonal Hexecontahedron
18. Velirina tessellation
description: Velirina tessellation
tessellation type: quadrilateral and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, Deltoidal hexecontahedron, Deltoidal icositetrahedron, Cube, Medial Rhombic Triacontahedron, Small Dodecacronic Hexecontahedron, Great Ditrigonal Dodecacronic Hexecontahedron, Triakis Icosahedron
19. Velirina tessellation
description: Velirina tessellation
tessellation type: quadrilateral and triangular
polyhedra: Rhombic dodecahedron, Möbius 10-akis dodecahedron, Rhombic hexecontahedron, Möbius hexakis icosahedron, Octahedron, Tetrakis hexahedron, Rhombic triacontahedron, Pentagonal dipyramid, Medial Deltoidal Hexecontahedron, Small Icosacronic Hexecontahedron, Great Rhombic Triacontahedron, Triakis Octahedron
20. Goshashka tessellation
description: Goshashka tessellation
tessellation type: pentagonal
polyhedra: Pentagonal icositetrahedron, Tetartoid, Pentagonal hexecontahedron, Dodecahedron, Great Dodecahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron, Small Ditrigonal Icosidodecahedron, Ditrigonal Dodecadodecahedron, Snub Icosidodecadodecahedron, Great Ditrigonal Dodecicosidodecahedron
21. Goshashka tessellation
description: Goshashka tessellation
tessellation type: pentagonal
polyhedra: Snub Dodecadodecahedron, Medial Pentagonal Hexecontahedron, Dodecadodecahedron, Great Ditrigonal Icosidodecahedron, Great Icosidodecahedron, Icosidodecadodecahedron, Inverted Snub Dodecadodecahedron, Great Pentagonal Hexecontahedron, Great Inverted Pentagonal Hexecontahedron
22. Velirina tessellation
description: Velirina tessellation
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, Deltoidal hexecontahedron, Deltoidal icositetrahedron, Cube, Medial Deltoidal Hexecontahedron, Small Icosacronic Hexecontahedron, Great Rhombic Triacontahedron, Triakis Icosahedron
23. Velirina tessellation
description: Velirina tessellation
tessellation type: quadrilateral and triangular
polyhedra: Rhombic dodecahedron, Möbius 10-akis dodecahedron, Rhombic hexecontahedron, Möbius hexakis icosahedron, Octahedron, Tetrakis hexahedron, Rhombic triacontahedron, Pentagonal dipyramid, Medial Rhombic Triacontahedron, Small Dodecacronic Hexecontahedron, Great Ditrigonal Dodecacronic Hexecontahedron, Triakis tetrahedron
24. Goshashka tessellation
description: Goshashka tessellation
tessellation type: pentagonal
polyhedra: Pentagonal icositetrahedron, Tetartoid, Pentagonal hexecontahedron, Dodecahedron, Great Dodecahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron, Small Ditrigonal Icosidodecahedron, Ditrigonal Dodecadodecahedron, Snub Icosidodecadodecahedron, Great Ditrigonal Dodecicosidodecahedron
25. Goshashka tessellation
description: Goshashka tessellation
tessellation type: pentagonal
polyhedra: Snub Dodecadodecahedron, Medial Pentagonal Hexecontahedron, Dodecadodecahedron, Great Ditrigonal Icosidodecahedron, Great Icosidodecahedron, Icosidodecadodecahedron, Inverted Snub Dodecadodecahedron, Great Pentagonal Hexecontahedron, Great Inverted Pentagonal Hexecontahedron
26. Velirina tessellation
description: Velirina tessellation
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, Deltoidal hexecontahedron, Deltoidal icositetrahedron, Cube, Medial Rhombic Triacontahedron, Small Dodecacronic Hexecontahedron, Great Ditrigonal Dodecacronic Hexecontahedron, Triakis Icosahedron
27. Velirina tessellation
description: Velirina tessellation
tessellation type: triangular and quadrilateral
polyhedra: Rhombic dodecahedron, Möbius 10-akis dodecahedron, Rhombic hexecontahedron, Möbius hexakis icosahedron, Octahedron, Tetrakis hexahedron, Rhombic triacontahedron, Pentagonal dipyramid, Medial Deltoidal Hexecontahedron, Small Icosacronic Hexecontahedron, Great Rhombic Triacontahedron, Triakis Tetrahedron
28. Pentagonal tessellation
description: Pentagonal tessellation
tessellation type: pentagonal
polyhedra: Pentagonal icositetrahedron, Tetartoid, Pentagonal hexecontahedron, Dodecahedron, Great Dodecahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron, Small Ditrigonal Icosidodecahedron, Ditrigonal Dodecadodecahedron, Snub Icosidodecadodecahedron, Great Ditrigonal Dodecicosidodecahedron
29. Pentagonal tessellation
description: Pentagonal tessellation
tessellation type: pentagonal
polyhedra: Snub Dodecadodecahedron, Medial Pentagonal Hexecontahedron, Dodecadodecahedron, Great Ditrigonal Icosidodecahedron, Great Icosidodecahedron, Icosidodecadodecahedron, Inverted Snub Dodecadodecahedron, Great Pentagonal Hexecontahedron, Great Inverted Pentagonal Hexecontahedron
30. Velirina tessellation
description: Velirina tessellation
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, Deltoidal hexecontahedron, Deltoidal icositetrahedron, Cube, Medial Rhombic Triacontahedron, Small Dodecacronic Hexecontahedron, Great Ditrigonal Dodecacronic Hexecontahedron, Triakis Icosahedron
31. Velirina tessellation
description: Velirina tessellation
tessellation type: triangular and quadrilateral
polyhedra: Rhombic dodecahedron, Möbius 10-akis dodecahedron, Rhombic hexecontahedron, Möbius hexakis icosahedron, Octahedron, Tetrakis hexahedron, Rhombic triacontahedron, Pentagonal dipyramid, Medial Deltoidal Hexecontahedron, Small Icosacronic Hexecontahedron, Great Rhombic Triacontahedron, Triakis Octahedron
32. Pentagonal tessellation
description: Pentagonal tessellation
tessellation type: pentagonal
polyhedra: Pentagonal icositetrahedron, Tetartoid, Pentagonal hexecontahedron, Dodecahedron, Great Dodecahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron, Small Ditrigonal Icosidodecahedron, Ditrigonal Dodecadodecahedron, Snub Icosidodecadodecahedron, Great Ditrigonal Dodecicosidodecahedron
33. Pentagonal tessellation
description: Pentagonal tessellation
tessellation type: pentagonal
polyhedra: Snub Dodecadodecahedron, Medial Pentagonal Hexecontahedron, Dodecadodecahedron, Great Ditrigonal Icosidodecahedron, Great Icosidodecahedron, Icosidodecadodecahedron, Inverted Snub Dodecadodecahedron, Great Pentagonal Hexecontahedron, Great Inverted Pentagonal Hexecontahedron
34. Velirina tessellation
description: Velirina tessellation
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, Deltoidal hexecontahedron, Deltoidal icositetrahedron, Cube, Medial Rhombic Triacontahedron, Small Dodecacronic Hexecontahedron, Great Ditrigonal Dodecacronic Hexecontahedron, Triakis Icosahedron
35. Velirina tessellation
description: Velirina tessellation
tessellation type: triangular and quadrilateral
polyhedra: Rhombic dodecahedron, Möbius 10-akis dodecahedron, Rhombic hexecontahedron, Möbius hexakis icosahedron, Octahedron, Tetrakis hexahedron, Rhombic triacontahedron, Pentagonal dipyramid, Medial Deltoidal Hexecontahedron, Small Icosacronic Hexecontahedron, Great Rhombic Triacontahedron, Triakis Octahedron
36. Goshashka tessellation
description: Goshashka tessellation
tessellation type: pentagonal
polyhedra: Pentagonal icositetrahedron, Tetartoid, Pentagonal hexecontahedron, Dodecahedron, Great Dodecahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron, Small Ditrigonal Icosidodecahedron, Ditrigonal Dodecadodecahedron, Snub Icosidodecadodecahedron, Great Ditrigonal Dodecicosidodecahedron
37. Goshashka tessellation
description: Goshashka tessellation
tessellation type: pentagonal
polyhedra: Snub Dodecadodecahedron, Medial Pentagonal Hexecontahedron, Dodecadodecahedron, Great Ditrigonal Icosidodecahedron, Great Icosidodecahedron, Icosidodecadodecahedron, Inverted Snub Dodecadodecahedron, Great Pentagonal Hexecontahedron, Great Inverted Pentagonal Hexecontahedron
Tessellation - part 3: 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 3: polyhedra tessellation and visualization with Virtual Reality". Available in: <https://paulohscwb.github.io/tessellation/part3/>, September 2025.
References:
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/