Prismatorhombated dodecahedral honeycomb
Jump to navigation
Jump to search
| Prismatorhombated dodecahedral honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform, compact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Priddoh |
| Coxeter diagram | x5o3x4x (     ) |
| Elements | |
| Cells | 12N pentagonal prisms, 15N octagonal prisms, 5N truncated cubes, 2N small rhombicosidodecahedra |
| Faces | 40N triangles, 60N+60N squares, 24N pentagons, 30N octagons |
| Edges | 60N+120N+120N |
| Vertices | 120N |
| Vertex figure | Isosceles trapezoidal pyramid, base edge lengths 1, √2, (1+√5)/2, √2; lateral edge lengths √2, √2, √2+√2, √2+√2  |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Priddoh |
| Regiment | Priddoh |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | [5,3,4] |
| Convex | Yes |
The prismatorhombated dodecahedral honeycomb, also called the prismatotruncated order-5 cubic honeycomb, runcitruncated order-5 cubic honeycomb, or runcicantellated dodecahedral honeycomb, is a compact uniform tiling of 3D hyperbolic space. 1 pentagonal prism, 2 octagonal prisms, 1 truncated cube, and 1 small rhombicosidodecahedron meet at each vertex. As the name suggests, it can be derived by runcicantellation of the dodecahedral honeycomb or equivalently by runcitruncation of the order-5 cubic honeycomb.
External links[edit | edit source]
- Klitzing, Richard. "priddoh".
- Wikipedia contributors. "Runcitruncated 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 | |  | |