Bitruncated dodecahedral honeycomb
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| Bitruncated dodecahedral honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform, compact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Bitdoh |
| Coxeter diagram | o5x3x4o (     ) |
| Elements | |
| Cells | 5N truncated octahedra, 2N truncated icosahedra |
| Faces | 15N squares, 12N pentagons, 40N hexagons |
| Edges | 60N+60N |
| Vertices | 60N |
| Vertex figure | Digonal disphenoid, edge lengths √2 (base 1), (1+√5)/2 (base 2), and √3 (sides)  |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Bitdoh |
| Regiment | Bitdoh |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | [5,3,4] |
| Convex | Yes |
The bitruncated dodecahedral honeycomb, also known as tthe cubidodecahedral honeycomb or bitruncated order-5 cubic honeycomb is a compact uniform tiling of 3D hyperbolic space. 2 truncated octahedra and 2 truncated icosahedra meet at each vertex. As the name suggests, it can be derived by bitruncation of either the dodecahedral honeycomb or its dual order-5 cubic honeycomb.
Representations[edit | edit source]
A bitruncated dodecahedral honeycomb has the following Coxeter diagrams:
- o5x3x4o () (full symmetry)
- o5x3x *b3x (
) (half symmetry)
External links[edit | edit source]
- Klitzing, Richard. "bitdoh".
- Wikipedia contributors. "Bitruncated order-4 dodecahedral honeycomb".
| 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 | |  | |
