Rectified order-4 hexagonal tiling honeycomb
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| Rectified order-4 hexagonal tiling honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform, paracompact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Rishexah |
| Coxeter diagram | o6x3o4o (     ) |
| Elements | |
| Cells | NM octahedra, 4N trihexagonal tilings |
| Faces | 8NM triangles, 2NM hexagons |
| Edges | 12NM |
| Vertices | 3NM |
| Vertex figure | Square prism, edge lengths 1 (base) and √3 (side)  |
| Related polytopes | |
| Army | Rishexah |
| Regiment | Rishexah |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | [6,3,4] |
| Convex | Yes |
The rectified order-4 hexagonal tiling honeycomb is a paracompact uniform tiling of 3D hyperbolic space. 2 octahedra and 4 trihexagonal tilings meet at each vertex. It is paracompact because it has Euclidean trihexagonal tiling cells. As the name suggests, it can be derived by rectification of the order-4 hexagonal tiling honeycomb.
Representations[edit | edit source]
A rectified order-4 hexagonal tiling honeycomb has the following coxeter diagrams:
- o6x3o4o () (full symmetry)
- o3x6o *b3o (
) (half symmetry, has cuboid verf) - o4o3x3x3*b (
) (half symmetry, has square frustum verf) - x3o3x3o3*a3*c (
) (quarter symmetry, has rectangular trapezoprism verf)
External links[edit | edit source]
- Klitzing, Richard. "rishexah".
- Wikipedia contributors. "Rectified order-4 hexagonal tiling honeycomb".
- lllllllllwith10ls. "Category 4: Square Rectates" (#95).
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Order-4 hexagonal tiling honeycomb | shexah | {6,3,4} | |  |
| Truncated order-4 hexagonal tiling honeycomb | tishexah | t{6,3,4} | |  |
| Rectified order-4 hexagonal tiling honeycomb | rishexah | r{6,3,4} | | |
| Cubic-hexagonal tiling honeycomb | chexah | 2t{6,3,4} | |  |
| Rectified order-6 cubic honeycomb | rihach | r{4,3,6} | |  |
| Truncated order-6 cubic honeycomb | thach | t{4,3,6} | |  |
| Order-6 cubic honeycomb | hachon | {4,3,6} | |  |
| Small rhombated order-4 hexagonal tiling honeycomb | srishexah | rr{6,3,4} | |  |
| Great rhombated order-4 hexagonal tiling honeycomb | grishexah | tr{6,3,4} | |  |
| Small rhombated order-6 cubic honeycomb | srihach | rr{4,3,6} | |  |
| Great rhombated order-6 cubic honeycomb | grihach | tr{4,3,6} | |  |
| Small prismated order-4 hexagonal tiling honeycomb | sidpichexah | t0,3{6,3,4} | |  |
| Prismatorhombated order-6 cubic honeycomb | prihach | t0,1,3{6,3,4} | |  |
| Prismatorhombated order-4 hexagonal tiling honeycomb | prishexah | t0,1,3{4,3,6} | |  |
| Great prismated order-4 hexagonal tiling honeycomb | gidpichexah | t0,1,2,3{6,3,4} | |  |