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From Wikipedia, the free encyclopedia
In geometry, the snub triapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of sr{∞,3}.
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 |
Drawn in chiral pairs, with edges missing between black triangles:
The dual 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.
n32 symmetry mutations of snub tilings: 3.3.3.3.n | ||||||||
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Symmetry n32 |
Spherical | Euclidean | Compact hyperbolic | Paracomp. | ||||
232 | 332 | 432 | 532 | 632 | 732 | 832 | ∞32 | |
Snub figures |
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Config. | 3.3.3.3.2 | 3.3.3.3.3 | 3.3.3.3.4 | 3.3.3.3.5 | 3.3.3.3.6 | 3.3.3.3.7 | 3.3.3.3.8 | 3.3.3.3.∞ |
Gyro figures |
||||||||
Config. | V3.3.3.3.2 | V3.3.3.3.3 | V3.3.3.3.4 | V3.3.3.3.5 | V3.3.3.3.6 | V3.3.3.3.7 | V3.3.3.3.8 | V3.3.3.3.∞ |
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