Snub octaoctagonal tiling
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| 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.pngFile:CDel node.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.pngFile:CDel node.png. In this construction there is only one color of octagon.
Related polyhedra and tiling
| 4n2 symmetry mutations of snub tilings: 3.3.n.3.n | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Symmetry 4n2 |
Spherical | Euclidean | Compact hyperbolic | Paracompact | |||||||
| 222 | 322 | 442 | 552 | 662 | 772 | 882 | ∞∞2 | ||||
| Snub figures |
File:Digonal antiprism.png | File:Pseudoicosahedron-3.png | File:Uniform tiling 44-snub.png | File:Uniform tiling 552-snub.png | File:Uniform tiling 66-snub.png | File:Uniform tiling 77-snub.png | File:Uniform tiling 88-snub.png | File:Uniform tiling ii2-snub.png | |||
| Config. | 3.3.2.3.2 | 3.3.3.3.3 | 3.3.4.3.4 | 3.3.5.3.5 | 3.3.6.3.6 | 3.3.7.3.7 | 3.3.8.3.8 | 3.3.∞.3.∞ | |||
| Gyro figures |
File:Digonal trapezohedron.png | File:Pyritohedron.png | File:Tiling Dual Semiregular V3-3-4-3-4 Cairo Pentagonal.svg | File:Infinitely-infinite-order floret pentagonal tiling.png | |||||||
| Config. | V3.3.2.3.2 | V3.3.3.3.3 | V3.3.4.3.4 | V3.3.5.3.5 | V3.3.6.3.6 | V3.3.7.3.7 | V3.3.8.3.8 | V3.3.∞.3.∞ | |||
References
- 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
Wikimedia Commons has media related to Uniform tiling 3-3-8-3-8.
