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In geometry, the snub tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{5,4}.
Snub tetrapentagonal tiling | |
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![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic uniform tiling |
Vertex configuration | 3.3.4.3.5 |
Schläfli symbol | sr{5,4} or |
Wythoff symbol | | 5 4 2 |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [5,4]+, (542) |
Dual | Order-5-4 floret pentagonal tiling |
Properties | Vertex-transitive Chiral |
Drawn in chiral pairs, with edges missing between black triangles:
The dual is called an order-5-4 floret pentagonal tiling, defined by face configuration V3.3.4.3.5.
The snub tetrapentagonal tiling is fourth in a series of snub polyhedra and tilings with vertex figure 3.3.4.3.n.
4n2 symmetry mutations of snub tilings: 3.3.4.3.n | ||||||||
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Symmetry 4n2 |
Spherical | Euclidean | Compact hyperbolic | Paracomp. | ||||
242 | 342 | 442 | 542 | 642 | 742 | 842 | ∞42 | |
Snub figures |
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Config. | 3.3.4.3.2 | 3.3.4.3.3 | 3.3.4.3.4 | 3.3.4.3.5 | 3.3.4.3.6 | 3.3.4.3.7 | 3.3.4.3.8 | 3.3.4.3.∞ |
Gyro figures |
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Config. | V3.3.4.3.2 | V3.3.4.3.3 | V3.3.4.3.4 | V3.3.4.3.5 | V3.3.4.3.6 | V3.3.4.3.7 | V3.3.4.3.8 | V3.3.4.3.∞ |
Uniform pentagonal/square tilings | |||||||||||
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Symmetry: [5,4], (*542) | [5,4]+, (542) | [5+,4], (5*2) | [5,4,1+], (*552) | ||||||||
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{5,4} | t{5,4} | r{5,4} | 2t{5,4}=t{4,5} | 2r{5,4}={4,5} | rr{5,4} | tr{5,4} | sr{5,4} | s{5,4} | h{4,5} | ||
Uniform duals | |||||||||||
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V54 | V4.10.10 | V4.5.4.5 | V5.8.8 | V45 | V4.4.5.4 | V4.8.10 | V3.3.4.3.5 | V3.3.5.3.5 | V55 |
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