| 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 |
In geometry, the snub triapeirotrigonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of s{3,∞}.
Related polyhedra and tiling
edit| Paracompact hyperbolic uniform tilings in [(∞,3,3)] family | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Symmetry: [(∞,3,3)], (*∞33) | [(∞,3,3)]+, (∞33) | ||||||||||
|
|
|
|
|
|
|
| ||||
|
|
|
|
|
|
|
| ||||
|
|
|
|
|
|
|
| ||||
| (∞,∞,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 | |||||||||||
|
|
|
|
|
|
|
| ||||
|
|
|
|
|
|
|
|
| ||||
|
|
||||||||||
| V(3.∞)3 | V3.∞.3.∞ | V(3.∞)3 | V3.6.∞.6 | V(3.3)∞ | V3.6.∞.6 | V6.6.∞ | V3.3.3.3.3.∞ | ||||
References
edit- 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
edit
Wikimedia Commons has media related to Uniform tiling 3-3-3-3-3-i.
External links
edit- 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
 | This hyperbolic geometry-related article is a stub. You can help Wikipedia by expanding it. |