Rectified square tiling honeycomb
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| Rectified square tiling honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform, paracompact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Risquah |
| Coxeter diagram | o4x4o3o (    ) |
| Elements | |
| Cells | MN cubes, 6N square tilings |
| Faces | 3MN+6MN squares |
| Edges | 12MN |
| Vertices | 4MN |
| Vertex figure | Triangular prism, edge length √2 75px |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Risquah |
| Regiment | Risquah |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | [4,4,3] |
| Convex | Yes |
The rectified square tiling honeycomb is a paracompact quasiregular tiling of 3D hyperbolic space. 2 cubes and 3 square tilings (as rectified square tilings) meet at each vertex. It is paracompact because it has Euclidean square tiling cells. As the name suggests, it can be derived by rectification of the square tiling honeycomb.
Representations[edit | edit source]
A rectified square tiling honeycomb has the folowing Coxeter diagrams:
- o4x4o3o () (full symmetry)
- x4o4x4o () (as small rhombated order-4 square tiling honeycomb)
- x4o4x x4*b (
) (skewvert)
External links[edit | edit source]
- Klitzing, Richard. "risquah".
- Wikipedia contributors. "Rectified square tiling honeycomb".
- lllllllllwith10ls. "Category 3: Triangular Rectates" (#84).
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Square tiling honeycomb | squah | {4,4,3} | |  |
| Rectified square tiling honeycomb | risquah | r{4,4,3} | | |
| Rectified octahedral honeycomb | rocth | r{3,4,4} | |  |
| Octahedral honeycomb | octh | {3,4,4} | |  |
| Truncated square tiling honeycomb | tisquah | t{4,4,3} | |  |
| Small rhombated square tiling honeycomb | srisquah | rr{4,4,3} | |  |
| Small prismated square tiling honeycomb | sidposquah | t0,3{4,4,3} | |  |
| Octahedral-square tiling honeycomb | osquah | 2t{4,4,3} | |  |
| Small rhombated octahedral honeycomb | srocth | rr{3,4,4} | |  |
| Truncated octahedral honeycomb | tocth | t{3,4,4} | |  |
| Great rhombated square tiling honeycomb | grisquah | tr{4,4,3} | |  |
| Prismatorhombated octahedral honeycomb | procth | t0,1,3{4,4,3} | |  |
| Prismatorhombated square tiling honeycomb | prisquah | t0,1,3{3,4,4} | |  |
| Great rhombated octahedral honeycomb | grocth | tr{3,4,4} | |  |
| Great prismated square tiling honeycomb | gidposquah | t0,1,2,3{4,4,3} | |  |