Trioctagonal tiling
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| Trioctagonal tiling | |
|---|---|
 | |
| Rank | 3 |
| Type | Uniform |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Toct |
| Coxeter diagram | o8x3o (    ) |
| Elements | |
| Faces | 8N triangles, 3N octagons |
| Edges | 24N |
| Vertices | 12N |
| Vertex figure | Rectangle, edge lengths 1 and √2+√2 |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Toct |
| Regiment | Toct |
| Dual | 8-3 rhombille tiling |
| Abstract & topological properties | |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | [8,3] |
| Convex | Yes |
The trioctagonal tiling or toct is a uniform tiling of the hyperbolic plane. 2 octagons and 2 triangles join at each vertex. It can be formed from the rectification of either the octagonal tiling or its dual order-8 triangular tiling.
Representations[edit | edit source]
A trioctagonal tiling has the following Coxeter diagrams:
- o8x3o () (full symmetry)
- o3x4x3*a (
) (half symmetry)
External links[edit | edit source]
- Klitzing, Richard. "toct".
- Wikipedia contributors. "Trioctagonal tiling".
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Octagonal tiling | ocat | {8,3} | |  |
| Trioctagonal tiling | toct | r{8,3} | |  |
| Order-8 triangular tiling | otrat | {3,8} | |  |
| Truncated octagonal tiling | tocat | t{8,3} | |  |
| Small rhombitrioctagonal tiling | srotoct | rr{8,3} | |  |
| Truncated order-8 triangular tiling | totrat | t{3,8} | |  |
| Great rhombitrioctagonal tiling | grotoct | tr{8,3} | |  |
| Snub trioctagonal tiling | snatoct | sr{8,3} |  |  |
