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Tetrapentagonal tiling
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In geometry, the tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1{4,5} or r{4,5}.
Tetrapentagonal tiling | |
---|---|
![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic uniform tiling |
Vertex configuration | (4.5)2 |
Schläfli symbol | r{5,4} or rr{5,5} or |
Wythoff symbol | 2 | 5 4 5 5 | 2 |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [5,4], (*542) [5,5], (*552) |
Dual | Order-5-4 rhombille tiling |
Properties | Vertex-transitive edge-transitive |
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Symmetry
A half symmetry [1+,4,5] = [5,5] construction exists, which can be seen as two colors of pentagons. This coloring can be called a rhombipentapentagonal tiling.
Dual tiling
The dual tiling is made of rhombic faces and has a face configuration V4.5.4.5:
Related polyhedra and tiling
See also
Wikimedia Commons has media related to Uniform tiling 4-5-4-5.
- Binary tiling, an aperiodic tiling of the hyperbolic plane by pentagons
- Uniform tilings in hyperbolic plane
- List of regular polytopes
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
- "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.
External links
- Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
- Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
- Hyperbolic and Spherical Tiling Gallery
- KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
- Hyperbolic Planar Tessellations, Don Hatch
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