Snub triapeirogonal tiling
| Snub triapeirogonal tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | 3.3.3.3.∞ |
| Schläfli symbol | sr{∞,3} or |
| Wythoff symbol | | ∞ 3 2 |
| Coxeter diagram |    or  
|
| Symmetry group | [∞,3]+, (∞32) |
| Dual | Order-3-infinite floret pentagonal tiling |
| Properties | Vertex-transitive Chiral |
In geometry, the snub triapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of sr{∞,3}.
Images
Drawn in chiral pairs, with edges missing between black triangles:
The dual tiling:
Related polyhedra and tiling
This hyperbolic tiling is topologically related as a part of sequence of uniform snub polyhedra with vertex configurations (3.3.3.3.n), and [n,3] Coxeter group symmetry. Template:Snub table Template:Order i-3 tiling table
See also
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 Search this book on
. (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. Search this book on
External links
- Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
- Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
Template:Hyperbolic-geometry-stub
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