Order-6 square tiling
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| Order-6 square tiling | |
|---|---|
 | |
| Rank | 3 |
| Type | Regular |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | |
| Coxeter diagram | o6o4x (    ) |
| Schläfli symbol | {4,6} |
| Elements | |
| Faces | 3N squares |
| Edges | 6N |
| Vertices | 2N |
| Vertex figure | Hexagon, edge length √2 |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Hisquat |
| Regiment | Hisquat |
| Dual | Order-4 hexagonal tiling |
| Halving | Order-6 hexagonal tiling |
| φ 2 | Order-3 apeirogonal tiling |
| Abstract & topological properties | |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | [6,4] |
| Convex | Yes |
The order-6 square tiling is a regular tiling of the hyperbolic plane. 6 squares join at each vertex.
This tiling can be alternated to produce the regular order-6 hexagonal tiling.
Representations[edit | edit source]
The order-6 square tiling has the following Coxeter diagrams:
- o6o4x () (full symmetry)
- o3o4x4*a (
) (squares of two types)
External links[edit | edit source]
- Klitzing, Richard. "Hisquat".
- Wikipedia contributors. "Order-6 square tiling".
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Order-4 hexagonal tiling | shexat | {6,4} | |  |
| Tetrahexagonal tiling | tehat | r{6,4} | |  |
| Order-6 square tiling | hisquat | {4,6} | |  |
| Truncated order-4 hexagonal tiling | toshexat | t{6,4} | |  |
| Small rhombitetrahexagonal tiling | srotehat | rr{6,4} | |  |
| Truncated order-6 square tiling | thisquat | t{4,6} | |  |
| Great rhombitetrahexagonal tiling | grotehat | tr{6,4} | |  |
| Snub tetrahexagonal tiling | snatehat | sr{6,4} |  |  |
