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 5
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 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. Quadrangular cross tessellation
description: quadrangular cross tessellation
tessellation type: quadrangular and triangular
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. Quadrangular cross tessellation
description: quadrangular cross tessellation
tessellation type: quadrangular and triangular
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, rhombic triacontahedron, pentagonal dipyramid, medial deltoidal hexecontahedron, Rhombicuboctahedron, Triakis Octahedron, Triakis Icosahedron
3. Quadrangular cross tessellation
description: quadrangular cross tessellation
tessellation type: quadrangular and triangular
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, triakis tetrahedron
4. Quadrangular tessellation
description: quadrangular tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron, deltoidal icositetrahedron, cube, great ditrigonal dodecacronic hexecontahedron, truncated dodecadodecahedron
5. Quadrangular tessellation
description: quadrangular tessellation
tessellation type: quadrangular and triangular
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, rhombic triacontahedron, pentagonal dipyramid, medial deltoidal hexecontahedron
6. Quadrangular tessellation
description: quadrangular tessellation
tessellation type: quadrangular and triangular
polyhedra: medial rhombic triacontahedron, small dodecacronic hexecontahedron, great hexacronic icositetrahedron, medial icosacronic hexecontahedron, rhombidodecadodecahedron, small icosacronic hexecontahedron, great rhombic triacontahedron, great rhombihexahedron, great rhombidodecahedron, Great Truncated Icosidodecahedron
7. Quadrangular arrow tessellation
description: quadrangular arrow tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron, deltoidal icositetrahedron, cube, great ditrigonal dodecacronic hexecontahedron
8. Quadrangular arrow tessellation
description: quadrangular arrow tessellation
tessellation type: quadrangular and triangular
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, rhombic triacontahedron, pentagonal dipyramid, medial deltoidal hexecontahedron, Truncated Dodecadodecahedron
9. Quadrangular arrow tessellation
description: quadrangular arrow tessellation
tessellation type: quadrangular and triangular
polyhedra: medial rhombic triacontahedron, small dodecacronic hexecontahedron, great hexacronic icositetrahedron, medial icosacronic hexecontahedron, rhombidodecadodecahedron, small icosacronic hexecontahedron, great rhombic triacontahedron, uniform great rhombicuboctahedron, great rhombihexahedron, great rhombidodecahedron, great truncated icosidodecahedron
10. Quadrangular arrow tessellation
description: quadrangular arrow tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron, deltoidal icositetrahedron, cube, great ditrigonal dodecacronic hexecontahedron
11. Quadrangular arrow tessellation
description: quadrangular arrow tessellation
tessellation type: quadrangular and triangular
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, rhombic triacontahedron, pentagonal dipyramid, medial deltoidal hexecontahedron, Truncated Dodecadodecahedron
12. Quadrangular arrow tessellation
description: quadrangular arrow tessellation
tessellation type: quadrangular and triangular
polyhedra: medial rhombic triacontahedron, small dodecacronic hexecontahedron, great hexacronic icositetrahedron, medial icosacronic hexecontahedron, rhombidodecadodecahedron, small icosacronic hexecontahedron, great rhombic triacontahedron, uniform great rhombicuboctahedron, great rhombihexahedron, great rhombidodecahedron, great truncated icosidodecahedron
13. Quadrangular tessellation
description: quadrangular tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron, deltoidal icositetrahedron, cube, great ditrigonal dodecacronic hexecontahedron, truncated dodecadodecahedron
14. Quadrangular tessellation
description: quadrangular tessellation
tessellation type: quadrangular and triangular
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, rhombic triacontahedron, pentagonal dipyramid, medial deltoidal hexecontahedron
15. Quadrangular tessellation
description: quadrangular tessellation
tessellation type: quadrangular and triangular
polyhedra: medial rhombic triacontahedron, small dodecacronic hexecontahedron, great hexacronic icositetrahedron, medial icosacronic hexecontahedron, rhombidodecadodecahedron, small icosacronic hexecontahedron, great rhombic triacontahedron, uniform great rhombicuboctahedron, great rhombihexahedron, great rhombidodecahedron, great truncated icosidodecahedron
16. Tessellation of a quadrangular mandala
description: tessellation of a quadrangular mandala
tessellation type: quadrangular and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron, deltoidal icositetrahedron, cube, great ditrigonal dodecacronic hexecontahedron, stella octangula, great rhombic triacontahedron, triakis tetrahedron
17. Tessellation of a quadrangular mandala
description: tessellation of a quadrangular mandala
tessellation type: quadrangular and triangular
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, medial rhombic triacontahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, small dodecacronic hexecontahedron, pentagonal dipyramid, medial deltoidal hexecontahedron, small icosacronic hexecontahedron, triakis octahedron, triakis icosahedron
18. 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
19. 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
20. Pentagrammic mandala tessellation
description: pentagrammic 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
21. Pentagrammic mandala tessellation
description: pentagrammic 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
22. Pentagonal floral mandala tessellation
description: pentagonal floral 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
23. Pentagonal floral mandala tessellation
description: pentagonal floral 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
24. Pentagonal mandala tessellation
description: pentagonal 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
25. Pentagonal mandala tessellation
description: pentagonal 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
26. Pentagrammic mandala tessellation
description: pentagrammic 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
27. Pentagrammic mandala tessellation
description: pentagrammic 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
28. Pentagonal mandala tessellation
description: pentagonal 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
29. Pentagonal mandala tessellation
description: pentagonal 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
30. Pentagonal mandala tessellation
description: pentagonal 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
31. Pentagonal mandala tessellation
description: pentagonal 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
32. Hexagonal tessellation
description: hexagonal tessellation
tessellation type: hexagonal
polyhedra: cubitruncated cuboctahedron, great dodecahemicosahedron, great dodecicosahedron, great truncated cuboctahedron, great truncated icosidodecahedron, icositruncated dodecadodecahedron, octahemioctahedron
33. Hexagonal tessellation
description: hexagonal tessellation
tessellation type: hexagonal
polyhedra: rhombicosahedron, small dodecicosahedron, small hexagonal hexecontahedron, small triambic icosahedron, great truncated icosahedron, truncated icosahedron, truncated tetrahedron, truncated octahedron
34. Snowflake tessellation
description: snowflake tessellation
tessellation type: hexagonal
polyhedra: cubitruncated cuboctahedron, great dodecahemicosahedron, great dodecicosahedron, great truncated cuboctahedron, great truncated icosidodecahedron, icositruncated dodecadodecahedron, octahemioctahedron
35. Snowflake tessellation
description: snowflake tessellation
tessellation type: hexagonal
polyhedra: rhombicosahedron, small dodecicosahedron, small hexagonal hexecontahedron, small triambic icosahedron, great truncated icosahedron, truncated icosahedron, truncated tetrahedron, truncated octahedron
36. Curitiba sidewalk tessellation
description: Curitiba sidewalk tessellation
tessellation type: quadrangular and triangular
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
37. Curitiba sidewalk tessellation
description: Curitiba sidewalk tessellation
tessellation type: quadrangular and triangular
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombic hexecontahedron, Möbius hexakis icosahedron, tetrakis hexahedron, rhombic triacontahedron, pentagonal dipyramid, medial deltoidal hexecontahedron
38. Curitiba sidewalk tessellation
description: Curitiba sidewalk tessellation
tessellation type: quadrangular and triangular
polyhedra: medial rhombic triacontahedron, small dodecacronic hexecontahedron, great hexacronic icositetrahedron, medial icosacronic hexecontahedron, rhombidodecadodecahedron, small icosacronic hexecontahedron, great rhombic triacontahedron, great rhombihexahedron, great rhombidodecahedron
Tessellation - part 5: 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 5: polyhedra tessellation and visualization with Virtual Reality". Available in: <https://paulohscwb.github.io/tessellation/part5/>, April 2026.
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/