Small prismatoicosahedral honeycomb
(Redirected from Small prismatodisicosahedral honeycomb)
| Small prismatoicosahedral honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform, compact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Spih |
| Coxeter diagram | x3o5o3x (    ) |
| Elements | |
| Cells | 10N triangular prisms, N icosahedra |
| Faces | 20N triangles, 15N squares |
| Edges | 30N |
| Vertices | 6N |
| Vertex figure | Pentagonal antiprism, edge lengths 1 (base) and √2 (sides)  |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Spih |
| Regiment | Spih |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | [[3,5,3]] |
| Convex | Yes |
The small prismatoicosahedral honeycomb or spih, also called the small prismatodisicosahedral honeycomb or runcinated icosahedral honeycomb, is a compact uniform tiling of 3D hyperbolic space. 2 icosahedra and 10 triangular prisms meet at each vertex. As the name suggests, it can be derived by runcination of the icosahedral honeycomb.
Related polytopes[edit | edit source]
The square faces of the small prismatoicosahedral honeycomb form {4,10∣3}, a regular skew apeirohedron.
External links[edit | edit source]
- Klitzing, Richard. "spih".
- Wikipedia contributors. "Runcinated icosahedral honeycomb".
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Icosahedral honeycomb | ikhon | {3,5,3} | |  |
| Rectified icosahedral honeycomb | rih | r{3,5,3} | |  |
| Rectified icosahedral honeycomb | rih | r{3,5,3} | | |
| Icosahedral honeycomb | ikhon | {3,5,3} | | |
| Truncated icosahedral honeycomb | tih | t{3,5,3} | |  |
| Small rhombated icosahedral honeycomb | srih | rr{3,5,3} | |  |
| Small prismated icosahedral honeycomb | spih | t0,3{3,5,3} | | |
| Disicosahedral honeycomb | dih | 2t{3,5,3} | |  |
| Small rhombated icosahedral honeycomb | srih | rr{3,5,3} | | |
| Truncated icosahedral honeycomb | tih | t{3,5,3} | | |
| Great rhombated icosahedral honeycomb | grih | tr{3,5,3} | |  |
| Prismatorhombated icosahedral honeycomb | prih | t0,1,3{3,5,3} | |  |
| Prismatorhombated icosahedral honeycomb | prih | t0,2,3{3,5,3} | | |
| Great rhombated icosahedral honeycomb | grih | tr{3,5,3} | | |
| Great prismated icosahedral honeycomb | gipiddih | t0,1,2,3{3,5,3} | |  |
| Partially diminished icosahedral honeycomb | pidih |  | ||