Rectified order-5 hexagonal tiling honeycomb
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| Rectified order-5 hexagonal tiling honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform, paracompact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Riphexah |
| Coxeter diagram | o6x3o5o (     ) |
| Elements | |
| Cells | NM icosahedra, 10N trihexagonal tilings |
| Faces | 20NM triangles, 5NM hexagons |
| Edges | 30NM |
| Vertices | 6NM |
| Vertex figure | Pentagonal prism, edge lengths 1 (base) and √3 (sides)  |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Riphexah |
| Regiment | Riphexah |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | [6,3,5] |
| Convex | Yes |
The rectified order-5 hexagonal tiling honeycomb is a paracompact uniform tiling of 3D hyperbolic space. 2 icosahedra and 5 trihexagonal tilings meet at each vertex. It is paracompact because it has Euclidean trihexagonal tiling cells. As the name suggests, it can be derived by rectification of the order-5 hexagonal tiling honeycomb.
Representations[edit | edit source]
A rectified order-5 hexagonal tiling honeycomb has the following Coxeter diagrams:
- o6x3o5o () (full symmetry)
- o5o3x3x3*b (
) (half symmetry)
External links[edit | edit source]
- Wikipedia contributors. "Rectified order-5 hexagonal tiling honeycomb".
- lllllllllwith10ls. "Category 5: Pentagonal Rectates" (#130).
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Order-5 hexagonal tiling honeycomb | phexah | {6,3,5} | |  |
| Rectified order-5 hexagonal tiling honeycomb | riphexah | r{6,3,5} | | |
| Rectified order-6 dodecahedral honeycomb | rihed | r{5,3,6} | |  |
| Order-6 dodecahedral honeycomb | hedhon | {5,3,6} | |  |
| Truncated order-5 hexagonal tiling honeycomb | tiphexah | t{6,3,5} | |  |
| Small rhombated order-5 hexagonal tiling honeycomb | sriphexah | rr{6,3,5} | |  |
| Small prismated order-5 hexagonal tiling honeycomb | sidpidohexah | t0,3{6,3,5} | |  |
| Dodecahedral-hexagonal tiling honeycomb | dohexah | 2t{6,3,5} | |  |
| Small rhombated order-6 dodecahedral honeycomb | srihed | rr{5,3,6} | |  |
| Truncated order-6 dodecahedral honeycomb | thed | t{5,3,6} | |  |
| Great rhombated order-5 hexagonal tiling honeycomb | griphexah | tr{6,3,5} | |  |
| Prismatorhombated order-6 dodecahedral honeycomb | prihed | t0,1,3{6,3,5} | |  |
| Prismatorhombated order-5 hexagonal tiling honeycomb | priphaxh | t0,1,3{5,3,6} | |  |
| Great rhombated order-6 dodecahedral honeycomb | grihed | tr{5,3,6} | |  |
| Great prismated order-5 hexagonal tiling honeycomb | gidpidohaxh | t0,1,2,3{6,3,5} | |  |