Order-6 dodecahedral honeycomb
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| Order-6 dodecahedral honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Type | Regular, paracompact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Hedhon |
| Coxeter diagram | x5o3o6o (     ) |
| Schläfli symbol | {5,3,6} |
| Elements | |
| Cells | NM dodecahedra |
| Faces | 6NM pentagons |
| Edges | 5NM |
| Vertices | 10N |
| Vertex figure | Triangular tiling, edge length (1+√5)/2 |
| Measures (edge length 1) | |
| Circumradius | 0 |
| Related polytopes | |
| Army | Hedhon |
| Regiment | Hedhon |
| Dual | Order-5 hexagonal tiling honeycomb |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | [6,3,5] |
| Convex | Yes |
The order-6 dodecahedral honeycomb is a paracompact regular tiling of 3D hyperbolic space. 6 ideal dodecahedra meet at each edge. All vertices are ideal points at infinity, with infinitely many dodecahedra meeting at each vertex in a triangular tiling arrangement.
Representations[edit | edit source]
An order-6 dodecahedral honeycomb has the followig Coxeter diagrams:
- x5o3o6o () (full symmetry)
- x5o3o3o3*b (
) (dodecahedra of two different types)
External links[edit | edit source]
- Klitzing, Richard. "hedhon".
- Wikipedia contributors. "Order-6 dodecahedral honeycomb".
- lllllllllwith10ls. "Category 1: Regulars" (#10).
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Order-5 hexagonal tiling honeycomb | phexah | {6,3,5} | |  |
| Rectified order-5 hexagonal tiling honeycomb | riphexah | r{6,3,5} | |  |
| Rectified order-6 dodecahedral honeycomb | rihed | r{5,3,6} | |  |
| Order-6 dodecahedral honeycomb | hedhon | {5,3,6} | | |
| Truncated order-5 hexagonal tiling honeycomb | tiphexah | t{6,3,5} | |  |
| Small rhombated order-5 hexagonal tiling honeycomb | sriphexah | rr{6,3,5} | |  |
| Small prismated order-5 hexagonal tiling honeycomb | sidpidohexah | t0,3{6,3,5} | |  |
| Dodecahedral-hexagonal tiling honeycomb | dohexah | 2t{6,3,5} | |  |
| Small rhombated order-6 dodecahedral honeycomb | srihed | rr{5,3,6} | |  |
| Truncated order-6 dodecahedral honeycomb | thed | t{5,3,6} | |  |
| Great rhombated order-5 hexagonal tiling honeycomb | griphexah | tr{6,3,5} | |  |
| Prismatorhombated order-6 dodecahedral honeycomb | prihed | t0,1,3{6,3,5} | |  |
| Prismatorhombated order-5 hexagonal tiling honeycomb | priphaxh | t0,1,3{5,3,6} | |  |
| Great rhombated order-6 dodecahedral honeycomb | grihed | tr{5,3,6} | |  |
| Great prismated order-5 hexagonal tiling honeycomb | gidpidohaxh | t0,1,2,3{6,3,5} | |  |