Tetrahexagonal tiling
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| Tetrahexagonal tiling | |
|---|---|
 | |
| Rank | 3 |
| Type | Uniform |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Tehat |
| Coxeter diagram | o6x4o (    ) |
| Elements | |
| Faces | 3N squares, 2N hexagons |
| Edges | 12N |
| Vertices | 6N |
| Vertex figure | Rectangle, edge lengths √2 and √3 |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Tehat |
| Regiment | Tehat |
| Dual | 6-4 rhombille tiling |
| Abstract & topological properties | |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | [6,4] |
| Convex | Yes |
The tetrahexagonal tiling, or tehat, is a uniform tiling of the hyperbolic plane. 2 hexagons and 2 squares join at each vertex. It can be formed by rectification of either the order-4 hexagonal tiling or its dual order-6 square tiling.
Representations[edit | edit source]
The tetrahexagonal tiling has the following Coxeter diagrams:
- o6x4o () (main symmetry)
- x6o6x () (cantellated order-6 hexagonal tiling, hexagons of two types)
- o3x4x4*a (
) ((4,4,3) symmetry, squares of two types) - x3xØx3xØ*a (
) (*3232 symmetry, both squares and hexagons of two types)
External links[edit | edit source]
- Klitzing, Richard. "tehat".
- Wikipedia contributors. "Tetrahexagonal 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} |  |  |
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Order-6 hexagonal tiling | hihat | {6,6} | |  |
| Rectified order-6 hexagonal tiling = Order-4 hexagonal tiling | shexat | r{6,6} | |  |
| Order-6 hexagonal tiling | hihat | {6,6} | |  |
| Truncated order-6 hexagonal tiling | thihat | t{6,6} | |  |
| Small rhombihexahexagonal tiling = Tetrahexagonal tiling | tehat | rr{6,6} | |  |
| Truncated order-6 hexagonal tiling | thihat | t{6,6} | |  |
| Great rhombitetrahexagonal tiling = Truncated order-4 hexagonal tiling | toshexat | tr{6,6} | |  |
| Snub hexahexagonal tiling | shihat | sr{6,6} | |  |
