Snub triapeirotrigonal tiling
In geometry, the snub triapeirotrigonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of s{3,∞}.
| Snub triapeirotrigonal tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | 3.3.3.3.3.∞ |
| Schläfli symbol | s{3,∞} s(∞,3,3) |
| Wythoff symbol | | ∞ 3 3 |
| Coxeter diagram |        |
| Symmetry group | [(∞,3,3)]+, (∞33) |
| Dual | Order-i-3-3_t0 dual tiling |
| Properties | Vertex-transitive Chiral |
Related polyhedra and tiling
| Paracompact hyperbolic uniform tilings in [(∞,3,3)] family | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Symmetry: [(∞,3,3)], (*∞33) | [(∞,3,3)]+, (∞33) | ||||||||||
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| (∞,∞,3) | t0,1(∞,3,3) | t1(∞,3,3) | t1,2(∞,3,3) | t2(∞,3,3) | t0,2(∞,3,3) | t0,1,2(∞,3,3) | s(∞,3,3) | ||||
| Dual tilings | |||||||||||
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| V(3.∞)3 | V3.∞.3.∞ | V(3.∞)3 | V3.6.∞.6 | V(3.3)∞ | V3.6.∞.6 | V6.6.∞ | V3.3.3.3.3.∞ | ||||
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gollark: `[22:31:55] [Server thread/INFO] [railcraft]: Registered Mine Ore Generator at depth 30 called mine_zinc` appears in the logs.
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, 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
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Wikimedia Commons has media related to Uniform tiling 3-3-3-3-3-i. |
- Square tiling
- Uniform tilings in hyperbolic plane
- List of regular polytopes
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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