Snub pentahexagonal tiling
In this article we will delve into the fascinating world of Snub pentahexagonal tiling, exploring its origins, its relevance in today's society and its impact on different areas of life. Snub pentahexagonal tiling has been the subject of interest and debate throughout history, motivating philosophers, scientists, artists and people from all walks of life to delve deeper into its meaning and repercussions. Through a detailed analysis, we will examine the most relevant aspects of Snub pentahexagonal tiling, from its first manifestations to its presence today, with the aim of providing a comprehensive and enriching vision of this diverse and exciting topic.
| Snub pentahexagonal tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | 3.3.5.3.6 |
| Schläfli symbol | sr{6,5} or |
| Wythoff symbol | | 6 5 2 |
| Coxeter diagram |   
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| Symmetry group | +, (652) |
| Dual | Order-6-5 floret pentagonal tiling |
| Properties | Vertex-transitive Chiral |
In geometry, the snub pentahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{6,5}.
Images
Drawn in chiral pairs, with edges missing between black triangles:
Related polyhedra and tiling
| Uniform hexagonal/pentagonal tilings | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 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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| 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 | ||
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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