| Pentahexagonal tiling | |
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 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | (5.6 |
| Schläfli symbol | r{6,5} or |
| Wythoff symbol | 2 | 6 5 |
| Coxeter diagram |    
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| Symmetry group | , (*652) |
| Dual | Order-6-5 rhombille tiling |
| Properties | Vertex-transitive edge-transitive |
In geometry, the pentahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of r{6,5} or t1{6,5}.
Uniform colorings
Related polyhedra and tiling
| Uniform hexagonal/pentagonal tilings | |||||||||||
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| Symmetry: , (*652) | , (652) | , (5*3) | , (*553) | ||||||||
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| {6,5} | t{6,5} | r{6,5} | 2t{6,5}=t{5,6} | 2r{6,5}={5,6} | rr{6,5} | tr{6,5} | sr{6,5} | s{5,6} | h{6,5} | ||
| Uniform duals | |||||||||||
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| V6 | V5.12.12 | V5.6.5.6 | V6.10.10 | V5 | V4.5.4.6 | V4.10.12 | V3.3.5.3.6 | V3.3.3.5.3.5 | V(3.5) | ||
| *5n2 symmetry mutations of quasiregular tilings: (5.n) | ||||||||
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| Symmetry *5n2 |
Spherical | Hyperbolic | Paracompact | Noncompact | ||||
| *352 |
*452 |
*552 |
*652 |
*752 |
*852 ... |
*∞52 |
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| Figures | 
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| Config. | (5.3) | (5.4) | (5.5) | (5.6) | (5.7) | (5.8) | (5.∞) | (5.ni) |
| Rhombic figures |
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| Config. | V(5.3) | V(5.4) | V(5.5) | V(5.6) | V(5.7) | V(5.8) | V(5.∞) | V(5.∞) |
| Symmetry mutation of quasiregular tilings: (6.n) | |||||||||||
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| Symmetry *6n2 |
Euclidean | Compact hyperbolic | Paracompact | Noncompact | |||||||
| *632 |
*642 |
*652 |
*662 |
*762 |
*862 ... |
*∞62 |
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| Quasiregular figures configuration |
 6.3.6.3 |
 6.4.6.4 |
6.5.6.5 |
 6.6.6.6 |
 6.7.6.7 |
 6.8.6.8 |
 6.∞.6.∞ |
6.∞.6.∞ | |||
| Dual figures | |||||||||||
| Rhombic figures configuration |
 V6.3.6.3 |
 V6.4.6.4 |
V6.5.6.5 |
 V6.6.6.6 |
V6.7.6.7 |
 V6.8.6.8 |
 V6.∞.6.∞ |
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| reflective symmetry uniform tilings | ||||||
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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.
See also
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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