Octagonal tiling
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Octagonal tiling | |
---|---|
Rank | 3 |
Type | Regular |
Space | Hyperbolic |
Notation | |
Bowers style acronym | Ocat |
Coxeter diagram | x8o3o () |
Schläfli symbol | {8,3} |
Elements | |
Faces | 3N octagons |
Edges | 12N |
Vertices | 8N |
Vertex figure | Triangle, edge length √2+√2 |
Measures (edge length 1) | |
Circumradius | |
Related polytopes | |
Army | Ocat |
Regiment | Ocat |
Dual | Order-8 triangular tiling |
Abstract & topological properties | |
Surface | Sphere |
Orientable | Yes |
Genus | 0 |
Properties | |
Symmetry | [8,3] |
Convex | Yes |
The order-3 octagonal tiling, or just octagonal tiling, is a regular tiling of the hyperbolic plane. 3 octagons join at each vertex.
It can be formed by truncating the order-8 square tiling.
Representations[edit | edit source]
The octagonal tiling has the following Coxeter diagrams:
- x8o3o () (main symmetry)
- o8x4x () (as truncated order-8 square tiling)
- x4x4x4*a () (octagons of three types)
External links[edit | edit source]
- Klitzing, Richard. "Ocat".
- Wikipedia contributors. "Octagonal tiling".