Dodecahedral honeycomb
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| Dodecahedral honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Type | Regular, compact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Doehon |
| Coxeter diagram | x5o3o4o (     ) |
| Schläfli symbol | {5,3,4} |
| Elements | |
| Cells | 2N dodecahedra |
| Faces | 12N pentagons |
| Edges | 15N |
| Vertices | 5N |
| Vertex figure | Octahedron, edge length (1+√5)/2  |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Doehon |
| Regiment | Doehon |
| Dual | Order-5 cubic honeycomb |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | [5,3,4] |
| Convex | Yes |
The order-4 dodecahedral honeycomb, or just dodecahedral honeycomb, is a compact regular tiling of 3D hyperbolic space. 4 dodecahedra meet at an edge, and 8 meet at a vertex.
Representations[edit | edit source]
A dodecahedral honeycomb has the following coxeter diagrams:
- x5o3o4o () (full symmetry)
- x5o3o *b3o (
) (half symmetry)
External links[edit | edit source]
- Klitzing, Richard. "Doehon".
- Wikipedia contributors. "Order-4 dodecahedral honeycomb".
- lllllllllwith10ls. "Category 1: Regulars" (#2).
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Dodecahedral honeycomb | doehon | {5,3,4} | | |
| Rectified dodecahedral honeycomb | riddoh | r{5,3,4} | |  |
| Rectified order-5 cubic honeycomb | ripech | r{4,3,5} | |  |
| Order-5 cubic honeycomb | pechon | {4,3,5} | |  |
| Truncated dodecahedral honeycomb | tiddoh | t{5,3,4} | |  |
| Small rhombated dodecahedral honeycomb | sriddoh | rr{5,3,4} | |  |
| Small prismated dodecahedral honeycomb | sidpicdoh | t0,3{5,3,4} | |  |
| Cubic-dodecahedral honeycomb | ciddoh | 2t{5,3,4} | |  |
| Small rhombated order-5 cubic honeycomb | sripech | rr{4,3,5} | |  |
| Truncated order-5 cubic honeycomb | tipech | t{4,3,5} | |  |
| Great rhombated dodecahedral honeycomb | griddoh | tr{5,3,4} | |  |
| Prismatorhombated order-5 cubic honeycomb | pripech | t0,1,3{5,3,4} | |  |
| Prismatorhombated dodecahedral honeycomb | priddoh | t0,1,3{4,3,5} | |  |
| Great rhombated order-5 cubic honeycomb | gripech | tr{4,3,5} | |  |
| Great prismated dodecahedral honeycomb | gidpicdoh | t0,1,2,3{5,3,4} | |  |
| Order-5 demicubic honeycomb | phachon | s{5,3,4} |  |  |
| Truncated order-5 demicubic honeycomb | tophach | |  | |
| Small rhombated order-5 demicubic honeycomb | sirphach | |  | |
| Great rhombated order-5 demicubic honeycomb | girphach | |  | |
