Triapeirogonal tiling
| Triapeirogonal tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | (3.∞)2 |
| Schläfli symbol | r{∞,3} or |
| Wythoff symbol | 2 | ∞ 3 |
| Coxeter diagram |     or  Error creating thumbnail: File:CDel labelinfin.pngFile:CDel branch 11.pngFile:CDel split2.png
|
| Symmetry group | [∞,3], (*∞32) |
| Dual | Order-3-infinite rhombille tiling |
| Properties | Vertex-transitive edge-transitive |
In geometry, the triapeirogonal tiling (or trigonal-horocyclic tiling) is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r{∞,3}.
Uniform colorings
The half-symmetry form, File:CDel labelinfin.pngFile:CDel branch 11.pngFile:CDel split2.png, has two colors of triangles:
Related polyhedra and tiling
This hyperbolic tiling is topologically related as a part of sequence of uniform quasiregular polyhedra with vertex configurations (3.n.3.n), and [n,3] Coxeter group symmetry. Template:Quasiregular3 table Template:Order i-3 tiling table Template:Order i-3-3 tiling table
See also
 |
Wikimedia Commons has media related to Uniform tiling 3-i-3-i. |
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.
- http://bendwavy.org/klitzing/incmats/o3xinfino.htm
- Klitzing, Richard. "2D Non-Compact Tilings". o3x∞o
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