Prismatorhombated tetrahedral honeycomb
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| Prismatorhombated tetrahedral honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform, paracompact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Prath |
| Coxeter diagram | x6x3o3x (    ) |
| Elements | |
| Cells | 2MN triangular prisms, MN cuboctahedra, MN dodecagonal prisms, 2N truncated hexagonal tilings |
| Faces | 4MN+4MN triangles, 6MN+6MN squares, 2MN dodecagons |
| Edges | 6MN+12MN+12MN |
| Vertices | 12MN |
| Vertex figure | Skewed rectangular pyramid, base edge lengths 1, √2, 1, √2; lateral edge lengths √2, √2, (√2+√6)/2, (√2+√6)/2  |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Prath |
| Regiment | Prath |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | [6,3,3] |
| Convex | Yes |
The prismatorhombated tetrahedral honeycomb, also called the runcitruncated hexagonal tiling honeycomb or runcicantellated tetrahedral honeycomb, is a paracompact uniform tiling of 3D hyperbolic space. 1 cuboctahedron, 1 truncated hexagonal tiling, 1 triangular prism, and 2 dodecagonal prisms meet at each vertex. It can be derived by runcitruncation of the hexagonal tiling honeycomb.
External links[edit | edit source]
- Wikipedia contributors. "Runcitruncated hexagonal tiling honeycomb".
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Hexagonal tiling honeycomb | hexah | {6,3,3} | |  |
| Truncated hexagonal tiling honeycomb | thexah | t{6,3,3} | |  |
| Rectified hexagonal tiling honeycomb | rihexah | r{6,3,3} | |  |
| Tetrahedral-hexagonal tiling honeycomb | tehexah | 2t{6,3,3} | |  |
| Rectified tetrahedral honeycomb | rath | r{3,3,6} | |  |
| Truncated tetrahedral honeycomb | tath | t{3,3,6} | |  |
| Tetrahedral honeycomb | thon | {3,3,6} | |  |
| Small rhombated hexagonal tiling honeycomb | srihexah | rr{6,3,3} | |  |
| Great rhombated hexagonal tiling honeycomb | grihexah | tr{6,3,3} | |  |
| Small rhombated tetrahedral honeycomb | srath | rr{3,3,6} | |  |
| Great rhombated tetrahedral honeycomb | grath | tr{3,3,6} | |  |
| Small prismated hexagonal tiling honeycomb | sidpithexah | t0,3{6,3,3} | |  |
| Prismatorhombated tetrahedral honeycomb | prath | t0,1,3{6,3,3} | | |
| Prismatorhombated hexagonal tiling honeycomb | prihexah | t0,1,3{3,3,6} | |  |
| Great prismated hexagonal tiling honeycomb | gidpithexah | t0,1,2,3{6,3,3} | |  |