Order-8 square tiling
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| Order-8 square tiling | |
|---|---|
 | |
| Rank | 3 |
| Type | Regular |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Osquat |
| Coxeter diagram | o8o4x (    ) |
| Schläfli symbol | {4,8} |
| Elements | |
| Faces | 2N squares |
| Edges | 4N |
| Vertices | N |
| Vertex figure | Octagon, edge length 1 |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Entrat |
| Regiment | Entrat |
| Dual | Order-4 octagonal tiling |
| Halving | Order-8 octagonal tiling |
| Abstract & topological properties | |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | [8,4] |
| Convex | Yes |
The order-8 square tiling is a regular tiling of the hyperbolic plane. 8 squares join at each vertex.
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Order-4 octagonal tiling | socat | {8,4} | |  |
| Tetraoctagonal tiling | teoct | r{8,4} | |  |
| Order-8 square tiling | osquat | {4,8} | |  |
| Truncated order-4 octagonal tiling | tosocat | t{8,4} | |  |
| Small rhombitetraoctagonal tiling | sroteoct | rr{8,4} | |  |
| Truncated order-8 square tiling = Octagonal tiling | ocat | t{4,8} | |  |
| Great rhombitetraoctagonal tiling | groteoct | tr{8,4} | |  |
| Snub tetraoctagonal tiling | snateoct | sr{8,4} |  |  |