Great prismatoicosahedral honeycomb
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| Great prismatoicosahedral honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform, compact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Gippih |
| Coxeter diagram | x3x5x3x (   ) |
| Elements | |
| Cells | 10N hexagonal prisms, N great rhombicosidodecahedra |
| Faces | 15N+30N squares, 20N hexagons, 6N decagons |
| Edges | 60N+60N |
| Vertices | 60N |
| Vertex figure | Phyllic disphenoid, edge lengths √2 (3), √3 (2), and √(5+√5)/2 (1) |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Gippih |
| Regiment | Gippih |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | [[3,5,3]] |
| Convex | Yes |
The great prismatoicosahedral honeycomb or gippih, also called the great prismatodisicosahedral honeycomb or omnitruncated icosahedral honeycomb, is a compact uniform tiling of 3D hyperbolic space. 2 great rhombicosidodecahedra and 2 hexagonal prisms meet at each vertex. As the name suggests, it can be derived by omnitruncation of the icosahedral honeycomb.
External links[edit | edit source]
- Klitzing, Richard. "gippih".
- Wikipedia contributors. "Omnitruncated 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 |  | ||