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 in strips
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 the faces of polyhedra, taking advantage of the rectangular symmetries of the faces of these solids.
On this page, we have some examples of tessellations in the form of strips, inserted into the rectangular faces of stellation to infinity polyhedra.
3D models
1. Rio de Janeiro sidewalk
description: Rio de Janeiro sidewalk pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
2. Curitiba sidewalk
description: Curitiba sidewalk pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
3. Rio de Janeiro sidewalk
description: Rio de Janeiro sidewalk pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
4. Flower of life
description: flower of life pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
5. Curitiba sidewalk
description: Curitiba sidewalk pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
6. Araucarias
description: Araucarias pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
7. Menger cross of Jerusalem
description: Menger cross of Jerusalem pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
8. Fractal tree
description: Fractal tree pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
9. Menger sponge
description: Menger sponge pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
10. Menger sponge
description: Menger sponge pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
11. Menger cross of Jerusalem
description: Menger cross of Jerusalem pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
12. Menger cross of Jerusalem
description: Menger cross of Jerusalem pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
13. Tree of life
description: tree of life pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
14. Intertwined curve
description: intertwined curve pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
15. Intertwined curve
description: intertwined curve pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
16. Lemniscata
description: lemniscata pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
17. Intertwined curve of three leaves
description: intertwined curve of three leaves pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
18. Four-leaf clover
description: four-leaf clover pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
19. Rosacea
description: rosacea pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
20. Butterfly
description: butterfly pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
21. Butterfly v2
description: butterfly pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
22. Elephant
description: Dorota Pankowska’s elephant pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
23. Whale
description: Dorota Pankowska’s whale pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
24. Frog
description: Dorota Pankowska’s frog pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
25. Monkey
description: Dorota Pankowska’s monkey pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
26. Owl
description: Dorota Pankowska’s owl pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
27. Toucan
description: Dorota Pankowska’s toucan pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
28. Giraffe
description: Dorota Pankowska’s giraffe pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
29. Mouse
description: Dorota Pankowska’s mouse pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
30. Dog
description: Dorota Pankowska’s dog pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
31. Cat
description: Dorota Pankowska’s cat pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
32. Fox
description: Dorota Pankowska’s fox pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
33. Walrus
description: Dorota Pankowska’s walrus pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
34. Rabbit
description: Dorota Pankowska’s rabbit pattern
tessellation type: rectangular
polyhedra: great dodecahemicosacron, great dodecahemidodecacron, hexahemioctacron, small icosihemidodecacron, tetrahemihexacron, star great dodecahemicosacron, star hexahemioctacron, star tetrahemihexacron
Tessellation in strips: 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 in strips: polyhedra tessellation and visualization with Virtual Reality". Available in: <https://paulohscwb.github.io/tessellation/strips/>, May 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/
Pankowska, D. “13 animals made from 13 circles”. https://dorotapankowska.com/13-animals-13-circles.html