Snub octaoctagonal tiling
| Snub octaoctagonal tiling | |
|---|---|
| Snub octaoctagonal tiling Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | 3.3.8.3.8 |
| Schläfli symbol | s{8,4} sr{8,8} |
| Wythoff symbol | | 8 8 2 |
| Coxeter diagram | File:CDel node h.pngFile:CDel 8.pngFile:CDel node h.pngFile:CDel 4.png File:CDel node h.pngFile:CDel 8.pngFile:CDel node h.pngFile:CDel 8.pngFile:CDel node h.png or File:CDel node h.pngFile:CDel split1-88.pngFile:CDel nodes hh.png |
| Symmetry group | [8,8]+, (882) [8+,4], (8*2) |
| Dual | Order-8-8 floret hexagonal tiling |
| Properties | Vertex-transitive |
In geometry, the snub octaoctagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{8,8}.
Images
Drawn in chiral pairs, with edges missing between black triangles:
Symmetry
A higher symmetry coloring can be constructed from [8,4] symmetry as s{8,4}, File:CDel node h.pngFile:CDel 8.pngFile:CDel node h.pngFile:CDel 4.png. In this construction there is only one color of octagon.
Related polyhedra and tiling
Template:Order 8-8 tiling table Template:Order 8-4 tiling table
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
See also
 |
Wikimedia Commons has media related to Uniform tiling 3-3-8-3-8. |
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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