Great rhombated dodecahedral honeycomb
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Great rhombated dodecahedral honeycomb | |
---|---|
Rank | 4 |
Type | Uniform, compact |
Space | Hyperbolic |
Notation | |
Bowers style acronym | Griddoh |
Coxeter diagram | x5x3x4o () |
Elements | |
Cells | 15N cubes, 5N truncated octahedra, 2N great rhombicosidodecahedra |
Faces | 30N+60N squares, 40N hexagons, 12N decagons |
Edges | 60N+60N+120N |
Vertices | 120N |
Vertex figure | Sphenoid edge lengths √2 (2), (1+√5)/2 (1), √3 (2), and √2+√2 (1) |
Measures (edge length 1) | |
Circumradius | |
Related polytopes | |
Army | Griddoh |
Regiment | Griddoh |
Abstract & topological properties | |
Orientable | Yes |
Properties | |
Symmetry | [5,3,4] |
Convex | Yes |
The great rhombated dodecahedral honeycomb, also called the cantitruncated dodecahedral honeycomb, is a compact uniform tiling of 3D hyperbolic space. 1 cube (as a square prism), 1 truncated octahedron, and 2 great rhombicosidodecahedra meet at each vertex. As the name suggests, it can be derived by cantitruncation of the dodecahedral honeycomb.
Representations[edit | edit source]
A great rhombated dodecahedral honeycomb has the following Coxeter diagrams:
- x5x3x4o () (full symmetry)
- x5x3x *b3x () (half symmetry)
External links[edit | edit source]
- Klitzing, Richard. "griddoh".
- Wikipedia contributors. "Cantitruncated order-4 dodecahedral honeycomb".