Snub triheptagonal tiling
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| Snub triheptagonal tiling | |
|---|---|
 | |
| Rank | 3 |
| Type | Uniform |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Snathet |
| Coxeter diagram | s7s3s (   ) |
| Elements | |
| Faces | 14N+42N triangles, 6N heptagons |
| Edges | 21N+42N+42N |
| Vertices | 42N |
| Vertex figure | Floret pentagon, edge lengths 1, 1, 1, 1, 2cos(π/7) |
| Measures (edge length 1) | |
| Circumradius | ≈ 2.64784 i |
| Surface area | Hyperbolic plane |
| Related polytopes | |
| Army | Snathet |
| Regiment | Snathet |
| Dual | Order 7-3 floret pentagonal tiling |
| Abstract & topological properties | |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | [7,3]+ |
| Convex | Yes |
The snub triheptagonal tiling or snathet, also called the snub heptagonal tiling, is a uniform tiling of the hyperbolic plane. 4 triangles and 1 heptagon join at each vertex. It can be formed by alternation of the great rhombitriheptagonal tiling, followed by adjustment of edge lengths to be all equal.
External links[edit | edit source]
- Klitzing, Richard. "snathet".
- Wikipedia contributors. "Snub triheptagonal tiling".
 truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Heptagonal tiling | heat | {7,3} |  |  |
| Triheptagonal tiling | thet | r{7,3} | |  |
| Order-7 triangular tiling | hetrat | {3,7} | |  |
| Truncated heptagonal tiling | theat | t{7,3} | |  |
| Small rhombitriheptagonal tiling | srothet | rr{7,3} | |  |
| Truncated order-7 triangular tiling | thetrat | t{3,7} | |  |
| Great rhombitriheptagonal tiling | grothet | tr{7,3} | |  |
| Snub triheptagonal tiling | snathet | sr{7,3} | | |