Bitruncated icosahedral honeycomb
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| Bitruncated icosahedral honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Dimension | 3 |
| Type | Uniform, compact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Bitih |
| Coxeter diagram | o3x5x3o (    ) |
| Elements | |
| Cells | N truncated dodecahedra |
| Faces | 10N triangles, 6N decagons |
| Edges | 30N |
| Vertices | 20N |
| Vertex figure | Tetragonal disphenoid, edge lengths 1 (base) and √(5+√5)/2 (sides)  |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Bitih |
| Regiment | Bitih |
| Abstract & topological properties | |
| Surface | Sphere |
| Orientable | Yes |
| Properties | |
| Symmetry | [[3,5,3]] |
| Convex | Yes |
The bitruncated icosahedral honeycomb or bitih, also known as the disicosahedral honeycomb, is a compact noble uniform tiling of 3D hyperbolic space. 4 truncated dodecahedra meet at each vertex. As the name suggests, it can be derived by bitruncation of the icosahedral honeycomb.
Related polytopes[edit | edit source]
The decagonal faces of the bitruncated icosahedral honeycomb form {10,4∣3}, a regular skew apeirohedron.
External links[edit | edit source]
- Klitzing, Richard. "bitih".
- Wikipedia contributors. "Bitruncated icosahedral honeycomb".
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Icosahedral honeycomb | ikhon | {3,5,3} | |  |
| Rectified icosahedral honeycomb | rih | r{3,5,3} | |  |
| Rectified icosahedral honeycomb | rih | r{3,5,3} | | |
| Icosahedral honeycomb | ikhon | {3,5,3} | | |
| Truncated icosahedral honeycomb | tih | t{3,5,3} | |  |
| Small rhombated icosahedral honeycomb | srih | rr{3,5,3} | |  |
| Small prismated icosahedral honeycomb | spih | t0,3{3,5,3} | |  |
| Disicosahedral honeycomb | dih | 2t{3,5,3} | | |
| Small rhombated icosahedral honeycomb | srih | rr{3,5,3} | | |
| Truncated icosahedral honeycomb | tih | t{3,5,3} | | |
| Great rhombated icosahedral honeycomb | grih | tr{3,5,3} | |  |
| Prismatorhombated icosahedral honeycomb | prih | t0,1,3{3,5,3} | |  |
| Prismatorhombated icosahedral honeycomb | prih | t0,2,3{3,5,3} | | |
| Great rhombated icosahedral honeycomb | grih | tr{3,5,3} | | |
| Great prismated icosahedral honeycomb | gipiddih | t0,1,2,3{3,5,3} | |  |
| Partially diminished icosahedral honeycomb | pidih |  | ||