Small rhombated order-5 demicubic honeycomb
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| Small rhombated order-5 demicubic honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform, compact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Sirphach |
| Coxeter diagram | x3o5o *b3x (     ) |
| Elements | |
| Cells | 5N tetrahedra, N dodecahedra, N small rhombicosidodecahedra |
| Faces | 20N triangles, 15N squares, 12N pentagons |
| Edges | 30N+30N |
| Vertices | 20N |
| Vertex figure | Triangular frustum, edge lengths 1 (top), (1+√5)/2 (base), and √2 (sides)  |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Sirphach |
| Regiment | Sirphach |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | [5,31,1] |
| Convex | Yes |
The small rhombated order-5 demicubic honeycomb or sirphach, also called the birectified alternated order-5 cubic honeycomb or runcic order-5 cubic honeycomb, is a compact uniform tiling of 3D hyperbolic space. 1 tetrahedron, 1 dodecahedron, and 3 small rhombicosidodecahedra meet at each vertex. It can be derived by birectification of the order-5 demicubic honeycomb.
Representations[edit | edit source]
A small rhombated order-5 demicubic honeycomb has the following Coxeter diagrams:
- x3o5o *b3x () (main symmetry)
- x5o3o4s (
) (as alternated faceting)
External links[edit | edit source]
- Klitzing, Richard. "sirphach".
- Wikipedia contributors. "Runcic order-5 cubic honeycomb".
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Dodecahedral honeycomb | doehon | {5,3,4} | |  |
| Rectified dodecahedral honeycomb | riddoh | r{5,3,4} | |  |
| Rectified order-5 cubic honeycomb | ripech | r{4,3,5} | |  |
| Order-5 cubic honeycomb | pechon | {4,3,5} | |  |
| Truncated dodecahedral honeycomb | tiddoh | t{5,3,4} | |  |
| Small rhombated dodecahedral honeycomb | sriddoh | rr{5,3,4} | |  |
| Small prismated dodecahedral honeycomb | sidpicdoh | t0,3{5,3,4} | |  |
| Cubic-dodecahedral honeycomb | ciddoh | 2t{5,3,4} | |  |
| Small rhombated order-5 cubic honeycomb | sripech | rr{4,3,5} | |  |
| Truncated order-5 cubic honeycomb | tipech | t{4,3,5} | |  |
| Great rhombated dodecahedral honeycomb | griddoh | tr{5,3,4} | |  |
| Prismatorhombated order-5 cubic honeycomb | pripech | t0,1,3{5,3,4} | |  |
| Prismatorhombated dodecahedral honeycomb | priddoh | t0,1,3{4,3,5} | |  |
| Great rhombated order-5 cubic honeycomb | gripech | tr{4,3,5} | |  |
| Great prismated dodecahedral honeycomb | gidpicdoh | t0,1,2,3{5,3,4} | |  |
| Order-5 demicubic honeycomb | phachon | s{5,3,4} | |  |
| Truncated order-5 demicubic honeycomb | tophach | |  | |
| Small rhombated order-5 demicubic honeycomb | sirphach | | | |
| Great rhombated order-5 demicubic honeycomb | girphach | |  | |