Truncated icosahedral honeycomb
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Truncated icosahedral honeycomb | |
---|---|
Rank | 4 |
Type | Uniform, compact |
Space | Hyperbolic |
Notation | |
Bowers style acronym | Tih |
Coxeter diagram | x3x5o3o () |
Elements | |
Cells | N dodecahedra, N truncated icosahedra |
Faces | 12N pentagons, 10N hexagons |
Edges | 10N+30N |
Vertices | 20N |
Vertex figure | Triangular pyramid, edge lengths (1+√5)/2 (base) and √3 (side) |
Measures (edge length 1) | |
Circumradius | |
Related polytopes | |
Army | Tih |
Regiment | Tih |
Abstract & topological properties | |
Orientable | Yes |
Properties | |
Symmetry | [3,5,3] |
Convex | Yes |
The truncated icosahedral honeycomb, or tih, is a compact uniform tiling of 3D hyperbolic space. 1 dodecahedron and 3 truncated icosahedra meet at each vertex. As the name suggests, it can be derived by truncation of the icosahedral honeycomb.
External links[edit | edit source]
- Klitzing, Richard. "tih".
- Wikipedia contributors. "Truncated icosahedral honeycomb".
- lllllllllwith10ls. "Category 2: Truncates" (#30).