Truncated dodecahedral honeycomb
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Truncated dodecahedral honeycomb | |
---|---|
Rank | 4 |
Type | Uniform, compact |
Space | Hyperbolic |
Notation | |
Bowers style acronym | Tidd |
Coxeter diagram | x5x3o4o () |
Elements | |
Cells | 5N octahedra, 2N truncated dodecahedra |
Faces | 40N triangles, 12N decagons |
Edges | 15N+60N |
Vertices | 30N |
Vertex figure | Square pyramid, edge lengths 1 (base) and (sides) |
Measures (edge length 1) | |
Circumradius | |
Related polytopes | |
Army | Tiddoh |
Regiment | Tiddoh |
Abstract & topological properties | |
Orientable | Yes |
Properties | |
Symmetry | [5,3,4] |
Convex | Yes |
The truncated dodecahedral honeycomb is a compact uniform tiling of 3D hyperbolic space. 1 octahedron and 4 truncated dodecahedra meet at each vertex. As the name suggests, it can be derived by truncation of the dodecahedral honeycomb.
Representations[edit | edit source]
A truncated dodecahedral honeycomb has the following Coxeter diagram:
- x5x3o4o () (full symmetry)
- x5x3o *b3o () (half symmetry)
External links[edit | edit source]
- Klitzing, Richard. "o4o3x5x".
- Wikipedia contributors. "Truncated order-4 dodecahedral honeycomb".
- lllllllllwith10ls. "Category 2: Truncates" (#31).