Prismatorhombated order-5 dodecahedral honeycomb
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| Prismatorhombated order-5 dodecahedral honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform, compact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Pripped |
| Coxeter diagram | x5x3o5x (    ) |
| Elements | |
| Cells | 6N pentagonal prisms, 6N decagonal prisms, N truncated dodecahedra, N small rhombicosidodecahedra |
| Faces | 20N triangles, 30N+30N squares, 12N pentagons, 12N decagons |
| Edges | 30N+60N+60N |
| Vertices | 60N |
| Vertex figure | Isosceles trapezoidal pyramid, base edge lengths 1, √2, (1+√5)/2, √2, side edge lengths √2,√2, √(5+√5)/2, √(5+√5)/2  |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Pripped |
| Regiment | Pripped |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | [5,3,5] |
| Convex | Yes |
The prismatorhombated order-5 dodecahedral honeycomb, also called the prismatotruncated order-5 dodecahedral honeycomb, runcitruncated order-5 dodecahedral honeycomb, or runcicantellated order-5 dodecahedral honeycomb, is a compact uniform tiling of 3D hyperbolic space. 1 pentagonal prism, 2 decagonal prisms, 1 truncated dodecahedron, and 1 small rhombicosidodecahedron meet at each vertex. As the names suggest, it can be derived by runcitruncation or equivalently runcicantellation of the order-5 dodecahedral honeycomb.
External links[edit | edit source]
- Klitzing, Richard. "pripped".
- Wikipedia contributors. "Runcitruncated order-5 dodecahedral honeycomb".
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Order-5 dodecahedral honeycomb | pedhon | {5,3,5} | |  |
| Rectified order-5 dodecahedral honeycomb | ripped | r{5,3,5} | |  |
| Rectified order-5 dodecahedral honeycomb | ripped | r{5,3,5} | | |
| Order-5 dodecahedral honeycomb | pedhon | {5,3,5} | | |
| Truncated order-5 dodecahedral honeycomb | tipped | t{5,3,5} | |  |
| Small rhombated order-5 dodecahedral honeycomb | sripped | rr{5,3,5} | |  |
| Small prismated order-5 dodecahedral honeycomb | spidded | t0,3{5,3,5} | |  |
| Disdodecahedral honeycomb | diddoh | 2t{5,3,5} | |  |
| Small rhombated order-5 dodecahedral honeycomb | sripped | rr{5,3,5} | | |
| Truncated order-5 dodecahedral honeycomb | tipped | t{5,3,5} | | |
| Great rhombated order-5 dodecahedral honeycomb | gripped | tr{5,3,5} | |  |
| Prismatorhombated order-5 dodecahedral honeycomb | pripped | t0,1,3{5,3,5} | | |
| Prismatorhombated order-5 dodecahedral honeycomb | pripped | t0,2,3{5,3,5} | | |
| Great rhombated order-5 dodecahedral honeycomb | gripped | tr{5,3,5} | | |
| Great prismated order-5 dodecahedral honeycomb | gipidded | t0,1,2,3{5,3,5} | |  |