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In geometry, the truncated order-4 pentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{5,4}.
| Truncated pentagonal tiling | |
|---|---|
Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | 4.10.10 |
| Schläfli symbol | t{5,4} |
| Wythoff symbol | 2 4 | 5 2 5 5 | |
| Coxeter diagram |     or   |
| Symmetry group | [5,4], (*542) [5,5], (*552) |
| Dual | Order-5 tetrakis square tiling |
| Properties | Vertex-transitive |
A half symmetry [1+,4,5] = [5,5] coloring can be constructed with two colors of decagons. This coloring is called a truncated pentapentagonal tiling.
There is only one subgroup of [5,5], [5,5]+, removing all the mirrors. This symmetry can be doubled to 542 symmetry by adding a bisecting mirror.
| *n42 symmetry mutation of truncated tilings: 4.2n.2n | |||||||||||
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| Symmetry *n42 [n,4] |
Spherical | Euclidean | Compact hyperbolic | Paracomp. | |||||||
| *242 [2,4] |
*342 [3,4] |
*442 [4,4] |
*542 [5,4] |
*642 [6,4] |
*742 [7,4] |
*842 [8,4]... |
*∞42 [∞,4] | ||||
| Truncated figures |
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| Config. | 4.4.4 | 4.6.6 | 4.8.8 | 4.10.10 | 4.12.12 | 4.14.14 | 4.16.16 | 4.∞.∞ | |||
| n-kis figures |
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| Config. | V4.4.4 | V4.6.6 | V4.8.8 | V4.10.10 | V4.12.12 | V4.14.14 | V4.16.16 | V4.∞.∞ | |||
| Uniform pentagonal/square tilings | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 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 | ||
| Uniform pentapentagonal tilings | |||||||||||
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| Symmetry: [5,5], (*552) | [5,5]+, (552) | ||||||||||
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| Order-5 pentagonal tiling {5,5} |
Truncated order-5 pentagonal tiling t{5,5} |
Order-4 pentagonal tiling r{5,5} |
Truncated order-5 pentagonal tiling 2t{5,5} = t{5,5} |
Order-5 pentagonal tiling 2r{5,5} = {5,5} |
Tetrapentagonal tiling rr{5,5} |
Truncated order-4 pentagonal tiling tr{5,5} |
Snub pentapentagonal tiling sr{5,5} | ||||
| Uniform duals | |||||||||||
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| Order-5 pentagonal tiling V5.5.5.5.5 |
V5.10.10 | Order-5 square tiling V5.5.5.5 |
V5.10.10 | Order-5 pentagonal tiling V5.5.5.5.5 |
V4.5.4.5 | V4.10.10 | V3.3.5.3.5 | ||||
 | This hyperbolic geometry-related article is a stub. You can help Wikipedia by expanding it. |
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