Snub pentapentagonal tiling
Snub pentapentagonal tiling | |
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![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic uniform tiling |
Vertex configuration | 3.3.5.3.5 |
Schläfli symbol | s{5,4} sr{5,5} |
Wythoff symbol | | 5 5 2 |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [5+,4], (5*2) [5,5]+, (552) |
Dual | Order-5-5 floret pentagonal tiling |
Properties | Vertex-transitive |
In geometry, the snub pentapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{5,5}, constructed from two regular pentagons and three equilateral triangles around every vertex.
Images
Drawn in chiral pairs, with edges missing between black triangles:
Symmetry
A double symmetry coloring can be constructed from [5,4] symmetry with only one color pentagon. It has Schläfli symbol s{5,4}, and Coxeter diagram .
Related tilings
Uniform pentapentagonal tilings
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Symmetry: [5,5], (*552) | [5,5]+, (552) | ||||||||||
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Order-5 pentagonal tiling {5,5} | Truncated order-5 pentagonal tiling t{5,5} | Order-4 pentagonal tiling r{5,5} | Truncated order-5 pentagonal tiling 2t{5,5} = t{5,5} | Order-5 pentagonal tiling 2r{5,5} = {5,5} | Tetrapentagonal tiling rr{5,5} | Truncated order-4 pentagonal tiling tr{5,5} | Snub pentapentagonal tiling sr{5,5} | ||||
Uniform duals | |||||||||||
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Order-5 pentagonal tiling V5.5.5.5.5 | V5.10.10 | Order-5 square tiling V5.5.5.5 | V5.10.10 | Order-5 pentagonal tiling V5.5.5.5.5 | V4.5.4.5 | V4.10.10 | V3.3.5.3.5 |
Uniform pentagonal/square tilings
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Symmetry: [5,4], (*542) | [5,4]+, (542) | [5+,4], (5*2) | [5,4,1+], (*552) | ||||||||
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{5,4} | t{5,4} | r{5,4} | 2t{5,4}=t{4,5} | 2r{5,4}={4,5} | rr{5,4} | tr{5,4} | sr{5,4} | s{5,4} | h{4,5} | ||
Uniform duals | |||||||||||
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V54 | V4.10.10 | V4.5.4.5 | V5.8.8 | V45 | V4.4.5.4 | V4.8.10 | V3.3.4.3.5 | V3.3.5.3.5 | V55 |
4n2 symmetry mutations of snub tilings: 3.3.n.3.n | |||||||||||
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Symmetry 4n2 | Spherical | Euclidean | Compact hyperbolic | Paracompact | |||||||
222 | 322 | 442 | 552 | 662 | 772 | 882 | ∞∞2 | ||||
Snub figures | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | |||
Config. | 3.3.2.3.2 | 3.3.3.3.3 | 3.3.4.3.4 | 3.3.5.3.5 | 3.3.6.3.6 | 3.3.7.3.7 | 3.3.8.3.8 | 3.3.∞.3.∞ | |||
Gyro figures | ![]() | ![]() | ![]() | ![]() | |||||||
Config. | V3.3.2.3.2 | V3.3.3.3.3 | V3.3.4.3.4 | V3.3.5.3.5 | V3.3.6.3.6 | V3.3.7.3.7 | V3.3.8.3.8 | V3.3.∞.3.∞ |
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 3-3-5-3-5.
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