Truncated order-5 pentagonal tiling
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| Truncated order-5 pentagonal tiling | |
|---|---|
 | |
| Rank | 3 |
| Type | Uniform |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Topepat |
| Coxeter diagram | x5x5o (   ) |
| Elements | |
| Faces | 2N pentagons, 2N decagons |
| Edges | 5N+10N |
| Vertices | 10N |
| Vertex figure | Isosceles triangle, edge lengths (1+√5)/2, √(5+√5)/2, √(5+√5)/2 |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Topepat |
| Regiment | Topepat |
| Dual | Pentakis order-5 pentagonal tiling |
| Abstract & topological properties | |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | [5,5] |
| Convex | Yes |
The truncated order-5 pentagonal tiling or topepat is a uniform tiling of the hyperbolic plane. 2 decagons and 1 pentagon join at each vertex. As the name suggests, it can be formed from the truncation of the order-5 pentagonal tiling.
Representations[edit | edit source]
A truncated order-5 pentagonal tiling has the following Coxeter diagrams:
- x5x5o () (main symmetry)
- x5o4s (
) (as alternated faceting)
External links[edit | edit source]
- Klitzing, Richard. "topepat".
- Wikipedia contributors. "Truncated order-5 pentagonal tiling".
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Order-5 pentagonal tiling | pepat | {5,5} | |  |
| Pentapentagonal tiling = Pentagonal tiling | peat | r{5,5} | |  |
| Order-5 pentagonal tiling | pepat | {5,5} | |  |
| Truncated order-5 pentagonal tiling | topepat | t{5,5} | |  |
| Small rhombipentapentagonal tiling = Tetrapentagonal tiling | tepet | rr{5,5} | |  |
| Truncated order-5 pentagonal tiling | topepat | t{5,5} | |  |
| Great rhombipentapentagonal tiling = Truncated pentagonal tiling | topeat | tr{5,5} | |  |
| Snub pentapentagonal tiling | spepat | sr{5,5} | |  |