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 6
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. 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
2. 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
3. Mandala pentagonal tessellation
description: mandala 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
4. Mandala pentagonal tessellation
description: mandala 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
5. Penrose triangle tessellation
description: Penrose triangle tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, great icosahedron, inverted snub dodecadodecahedron, stella octangula, tetrahedron, pentakis dodecahedron
6. Penrose triangle tessellation
description: Penrose triangle tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius 10-akis dodecahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, pentagonal dipyramid, icosahedron, small ditrigonal icosidodecahedron, snub dodecadodecahedron, snub icosidodecadodecahedron
7. Penrose triangle tessellation
description: Penrose triangle tessellation
tessellation type: quadrangular and triangular
polyhedra: great ditrigonal dodecicosidodecahedron, great dodecicosidodecahedron, great icosidodecahedron, great stellated truncated dodecahedron, small snub icosicosidodecahedron, stellated truncated hexahedron
8. Celtic knot tessellation
description: Celtic knot tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, great icosahedron, inverted snub dodecadodecahedron, stella octangula, tetrahedron, great ditrigonal dodecicosidodecahedron, pentakis dodecahedron
9. Celtic knot tessellation
description: Celtic knot tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius 10-akis dodecahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, pentagonal dipyramid, icosahedron, small ditrigonal icosidodecahedron, snub dodecadodecahedron, snub icosidodecadodecahedron
10. Celtic knot tessellation
description: Celtic knot tessellation
tessellation type: quadrangular and triangular
polyhedra: great ditrigonal dodecicosidodecahedron, great dodecicosidodecahedron, great icosidodecahedron, great stellated truncated dodecahedron, small snub icosicosidodecahedron, stellated truncated hexahedron
11. Triangular tessellation
description: triangular tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, great icosahedron, inverted snub dodecadodecahedron, stella octangula, tetrahedron, pentakis dodecahedron
12. Triangular tessellation
description: triangular tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius 10-akis dodecahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, pentagonal dipyramid, icosahedron, small ditrigonal icosidodecahedron, snub dodecadodecahedron, snub icosidodecadodecahedron
13. Triangular tessellation
description: triangular tessellation
tessellation type: quadrangular and triangular
polyhedra: great ditrigonal dodecicosidodecahedron, great dodecicosidodecahedron, great icosidodecahedron, great stellated truncated dodecahedron, small snub icosicosidodecahedron, stellated truncated hexahedron
14. Penrose triangle tessellation
description: Penrose triangle tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, great icosahedron, inverted snub dodecadodecahedron, stella octangula, tetrahedron, great ditrigonal dodecicosidodecahedron, pentakis dodecahedron
15. Penrose triangle tessellation
description: Penrose triangle tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius 10-akis dodecahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, pentagonal dipyramid, icosahedron, small ditrigonal icosidodecahedron, snub dodecadodecahedron, snub icosidodecadodecahedron
16. Triangular tessellation
description: triangular tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, great icosahedron, inverted snub dodecadodecahedron, stella octangula, tetrahedron, pentakis dodecahedron, triakis octahedron, triakis icosahedron
17. Triangular tessellation
description: triangular tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius 10-akis dodecahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, pentagonal dipyramid, icosahedron, small ditrigonal icosidodecahedron, snub dodecadodecahedron, snub icosidodecadodecahedron
18. Triangular tessellation
description: triangular tessellation
tessellation type: quadrangular and triangular
polyhedra: great ditrigonal dodecicosidodecahedron, great dodecicosidodecahedron, great icosidodecahedron, great stellated truncated dodecahedron, small snub icosicosidodecahedron, stellated truncated hexahedron, triakis tetrahedron
19. Pentagrammic tessellation
description: pentagrammic 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
20. Pentagrammic tessellation
description: pentagrammic 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
21. Celtic knot tessellation
description: Celtic knot tessellation
tessellation type: quadrangular and triangular
polyhedra: Escher solid, Möbius deltahedron, deltoidal hexecontahedron, deltoidal icositetrahedron, cube, great ditrigonal dodecacronic hexecontahedron, cuboctahedron, snub cube, square orthobicupola, great rhombihexahedron, great rhombidodecahedron
22. Celtic knot tessellation
description: Celtic knot tessellation
tessellation type: quadrangular and triangular
polyhedra: rhombic dodecahedron, rhombic hexecontahedron, octahedron, tetrakis hexahedron, rhombic triacontahedron, pentagonal dipyramid, medial deltoidal hexecontahedron, rhombicuboctahedron, tetrahemihexahedron, truncated dodecadodecahedron, great truncated icosidodecahedron
23. Celtic knot tessellation
description: Celtic knot tessellation
tessellation type: quadrangular and triangular
polyhedra: great dirhombicosidodecahedron, medial rhombic triacontahedron, small dodecacronic hexecontahedron, great hexacronic icositetrahedron, medial icosacronic hexecontahedron, rhombidodecadodecahedron, small icosacronic hexecontahedron, great rhombic triacontahedron, uniform great rhombicuboctahedron, triakis tetrahedron, triakis octahedron, triakis icosahedron
24. Celtic knot tessellation
description: Celtic knot tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, hexakis tetrahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron, deltoidal icositetrahedron, cube, truncated dodecadodecahedron
25. Celtic knot tessellation
description: Celtic knot tessellation
tessellation type: quadrangular and triangular
polyhedra: rhombic dodecahedron, Möbius 10-akis dodecahedron, rhombidodecadodecahedron, Möbius hexakis icosahedron, octahedron, tetrakis hexahedron, rhombic triacontahedron, great rhombihexahedron, great rhombidodecahedron
26. Octagrammic tessellation
description: octagrammic 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
27. Octagrammic tessellation
description: octagrammic 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
28. Octagrammic tessellation
description: octagrammic 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
29. 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
30. 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
31. Celtic knot tessellation
description: Celtic knot tessellation
tessellation type: quadrangular and triangular
polyhedra: Möbius hexakis octahedron, Escher solid, great dirhombicosidodecahedron, Möbius deltahedron, Möbius octakis hexahedron, deltoidal hexecontahedron, deltoidal icositetrahedron, cube, great ditrigonal dodecacronic hexecontahedron
32. Celtic knot tessellation
description: Celtic knot 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, great rhombihexahedron, great rhombidodecahedron
33. Celtic knot tessellation
description: Celtic knot 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, stella octangula, truncated dodecadodecahedron, great truncated icosidodecahedron
34. Pentagrammic tessellation
description: pentagrammic 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. Pentagrammic tessellation
description: pentagrammic 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
36. Hexagrammic tessellation
description: hexagrammic tessellation
tessellation type: hexagonal
polyhedra: cubitruncated cuboctahedron, great dodecahemicosahedron, great dodecicosahedron, great truncated cuboctahedron, great truncated icosidodecahedron, icositruncated dodecadodecahedron, octahemioctahedron
37. Hexagrammic tessellation
description: hexagrammic tessellation
tessellation type: hexagonal
polyhedra: rhombicosahedron, small dodecicosahedron, small hexagonal hexecontahedron, small triambic icosahedron, great truncated icosahedron, truncated icosahedron, truncated tetrahedron, truncated octahedron
Tessellation - part 6: 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 6: polyhedra tessellation and visualization with Virtual Reality". Available in: <https://paulohscwb.github.io/tessellation/part6/>, 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/