Heptagonal tiling
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| Heptagonal tiling | |
|---|---|
 | |
| Rank | 3 |
| Type | Regular |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Heat |
| Coxeter diagram | x7o3o (    ) |
| Schläfli symbol | {7,3} |
| Elements | |
| Faces | 6N Heptagons |
| Edges | 21N |
| Vertices | 14N |
| Vertex figure | Triangle, edge length 2cos(π/7) |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Heat |
| Regiment | Heat |
| Dual | Order-7 triangular tiling |
| Abstract & topological properties | |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | [7,3] |
| Convex | Yes |
The order-3 heptagonal tiling, or just heptagonal tiling or heat, is a regular tiling of the hyperbolic plane. 3 heptagons join at each vertex.
This tiling is the simplest tiling with three regular polygons at each vertex that neither fits in Euclidean space like the hexagonal tiling does, nor folds into spherical space like the dodecahedron (pentagons), cube (squares), or tetrahedron (triangles).
External links[edit | edit source]
- Wikipedia contributors. "Heptagonal tiling".
- Nan Ma. "Heptagonal tiling {7,3}".
| 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} |  |  |