Order-6 cubic honeycomb
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| Order-6 cubic honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Type | Regular, paracompact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Hachon |
| Coxeter diagram | o6o3o4x (     ) |
| Schläfli symbol | {4,3,6} |
| Elements | |
| Cells | NM cubes |
| Faces | 3NM squares |
| Edges | 2NM |
| Vertices | 4N |
| Vertex figure | Triangular tiling, edge length √2 |
| Measures (edge length 1) | |
| Circumradius | 0 |
| Related polytopes | |
| Army | Hachon |
| Regiment | Hachon |
| Dual | Order-4 hexagonal tiling honeycomb |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | [6,3,4] |
| Convex | Yes |
The order-6 cubic honeycomb is a paracompact regular tiling of 3D hyperbolic space. 6 ideal cubes meet at each edge. All vertices are ideal points at infinity, with infinitely many cubes meeting at each vertex in a triangular tiling arrangement.
This honeycomb can be alternated to produce the uniform alternated order-6 cubic honeycomb.
Representations[edit | edit source]
An order-6 cubic honeycomb has he following Coxeter diagrams:
- o6o3o4x () (full symmetry)
- x4o3o3o3*b (
) (cubes of two different types)
External links[edit | edit source]
- Klitzing, Richard. "hachon".
- Wikipedia Contributors. "Order-6 cubic honeycomb".
- lllllllllwith10ls. "Category 1: Regulars" (#8).
| 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} | |  |