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 4
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, Vibali, Eye-Psy, Goshashka and Gordon Dylan Johnson, 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. 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
2. 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
3. Gordon Dylan Johnson tessellation
description: Gordon Dylan Johnson 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
4. Gordon Dylan Johnson tessellation
description: Gordon Dylan Johnson 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
5. Square and triangle tessellation
description: Square and triangle tessellation
tessellation type: triangular and quadrilateral
polyhedra: Inverted Snub Dodecadodecahedron, Snub Icosidodecadodecahedron, Small Ditrigonal Icosidodecahedron, Uniform Great Rhombicuboctahedron, Great Ditrigonal Dodecacronic Hexecontahedron, Medial Deltoidal Hexecontahedron, Great Hexacronic Icositetrahedron
6. Square and triangle tessellation
description: Square and triangle tessellation
tessellation type: triangular and quadrilateral
polyhedra: Great Dirhombicosidodecahedron, Rhombicuboctahedron, Great Snub Dodecicosidodecahedron, Tetrahemihexahedron, Great Dodecacronic Hexecontahedron, Medial Rhombic Triacontahedron, Small Dodecacronic Hexecontahedron
7. Square and triangle tessellation
description: Square and triangle tessellation
tessellation type: triangular and quadrilateral
polyhedra: Great Icosacronic Hexecontahedron, Snub Cube, Small Icosacronic Hexecontahedron, Rhombidodecadodecahedron, Medial Icosacronic Hexecontahedron, Great Rhombic Triacontahedron
8. Square and triangle tessellation
description: Square and triangle tessellation
tessellation type: triangular and quadrilateral
polyhedra: Inverted Snub Dodecadodecahedron, Snub Icosidodecadodecahedron, Uniform Great Rhombicuboctahedron, Great Ditrigonal Dodecacronic Hexecontahedron, Medial Deltoidal Hexecontahedron, Great Hexacronic Icositetrahedron, Great Truncated Icosidodecahedron
9. Square and triangle tessellation
description: Square and triangle tessellation
tessellation type: triangular and quadrilateral
polyhedra: Great Dirhombicosidodecahedron, Rhombicuboctahedron, Tetrahemihexahedron, Great Dodecacronic Hexecontahedron, Medial Rhombic Triacontahedron, Small Dodecacronic Hexecontahedron, Great Rhombihexahedron, Truncated Dodecadodecahedron
10. Square and triangle tessellation
description: Square and triangle tessellation
tessellation type: quadrilateral and triangular
polyhedra: Great Icosacronic Hexecontahedron, Snub Cube, Small Icosacronic Hexecontahedron, Rhombidodecadodecahedron, Medial Icosacronic Hexecontahedron, Great Rhombic Triacontahedron, Great Rhombidodecahedron, Triakis tetrahedron, Triakis Octahedron, Triakis Icosahedron
11. 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
12. 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
13. Francine Champagne tessellation
description: Francine Champagne tessellation - Keep Mother Earth Clean
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, pentagonal dipyramid
14. 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
15. 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
16. Eye-Psy tessellation
description: Eye-Psy tessellation
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, pentagonal dipyramid, Icosahedron, Pentakis dodecahedron
17. 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
18. 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
19. Vibali tessellation
description: Vibali tessellation
tessellation type: quadrilateral and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, Hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, pentagonal dipyramid, Tetrahedron, Pentakis dodecahedron
20. Vibali tessellation
description: Vibali tessellation
tessellation type: quadrilateral and triangular
polyhedra: Möbius 10-akis dodecahedron, Möbius hexakis icosahedron, Octahedron, Tetrakis hexahedron, Stella octangula, Icosahedron
21. Pentagonal spiral tessellation
description: Pentagonal spiral 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
22. Pentagonal spiral tessellation
description: Pentagonal spiral 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
23. 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
24. 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 Hexecontahedrononal Dodecadodecahedron, Snub Icosidodecadodecahedron, Great Ditrigonal Dodecicosidodecahedron
25. Gordon Dylan Johnson tessellation
description: Gordon Dylan Johnson tessellation
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, Pentagonal dipyramid, Great Icosahedron
26. Gordon Dylan Johnson tessellation
description: Gordon Dylan Johnson tessellation
tessellation type: triangular and quadrilateral
polyhedra: Deltoidal hexecontahedron, Rhombic triacontahedron, Cube, Rhombic dodecahedron, Rhombic hexecontahedron, Deltoidal icositetrahedron, Great Dodecacronic Hexecontahedron, Great Rhombic Triacontahedron, Medial Deltoidal Hexecontahedron, Medial Icosacronic Hexecontahedron, Medial Rhombic Triacontahedron
27. Gordon Dylan Johnson tessellation
description: Gordon Dylan Johnson tessellation
tessellation type: triangular and quadrilateral
polyhedra: Rhombidodecadodecahedron, Small Dodecacronic Hexecontahedron, Great Icosacronic Hexecontahedron, Stella octangula, Truncated Dodecadodecahedron, Great Rhombihexahedron, Small Icosacronic Hexecontahedron, Great Rhombidodecahedron, Great Truncated Icosidodecahedron
28. 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
29. 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
30. Square tessellation
description: Square tessellation
tessellation type: triangular and quadrilateral
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, Deltoidal hexecontahedron, Deltoidal icositetrahedron, Cube, Pentagonal dipyramid
31. Square tessellation
description: Square tessellation
tessellation type: triangular and quadrilateral
polyhedra: Rhombic dodecahedron, Möbius 10-akis dodecahedron, Rhombic hexecontahedron, Möbius hexakis icosahedron, Octahedron, Tetrakis hexahedron, Rhombic triacontahedron, Stella octangula
32. Decagonal tessellation
description: Decagonal 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. Decagonal tessellation
description: Decagonal 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. 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
35. 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
Tessellation - part 4: 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 4: polyhedra tessellation and visualization with Virtual Reality". Available in: <https://paulohscwb.github.io/tessellation/part4/>, 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/