Pentahexagonal tiling
Pentahexagonal tiling | |
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![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic uniform tiling |
Vertex configuration | (5.62 |
Schläfli symbol | r{6,5} or |
Wythoff symbol | 2 | 6 5 |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [6,5], (*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: [6,5], (*652) | [6,5]+, (652) | [6,5+], (5*3) | [1+,6,5], (*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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V65 | V5.12.12 | V5.6.5.6 | V6.10.10 | V56 | V4.5.4.6 | V4.10.12 | V3.3.5.3.6 | V3.3.3.5.3.5 | V(3.5)5 |
*5n2 symmetry mutations of quasiregular tilings: (5.n)2
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Symmetry *5n2 [n,5] | Spherical | Hyperbolic | Paracompact | Noncompact | ||||
*352 [3,5] | *452 [4,5] | *552 [5,5] | *652 [6,5] | *752 [7,5] | *852 [8,5]... | *∞52 [∞,5] | [ni,5] | |
Figures | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | |
Config. | (5.3)2 | (5.4)2 | (5.5)2 | (5.6)2 | (5.7)2 | (5.8)2 | (5.∞)2 | (5.ni)2 |
Rhombic figures | ![]() | ![]() | ![]() | ![]() | ||||
Config. | V(5.3)2 | V(5.4)2 | V(5.5)2 | V(5.6)2 | V(5.7)2 | V(5.8)2 | V(5.∞)2 | V(5.∞)2 |
Symmetry mutation of quasiregular tilings: 6.n.6.n
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Symmetry *6n2 [n,6] | Euclidean | Compact hyperbolic | Paracompact | Noncompact | |||||||
*632 [3,6] | *642 [4,6] | *652 [5,6] | *662 [6,6] | *762 [7,6] | *862 [8,6]... | *∞62 [∞,6] | [iπ/λ,6] | ||||
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.∞ |
[(5,5,3)] 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
![](http://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png)
Wikimedia Commons has media related to Uniform tiling 5-6-5-6.
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