Small prismatohecatonicosidishecatonicosachoron
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Small prismatohecatonicosidishecatonicosachoron | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Siphidy |
Coxeter diagram | x5x3x5o5/3*b () |
Elements | |
Cells | 720 pentagonal prisms, 120 truncated great dodecahedra, 120 icosidodecadodecahedra, 120 great rhombicosidodecahedra |
Faces | 3600 squares, 1440 pentagons, 1440 pentagrams, 2400 hexagons, 1440 decagons |
Edges | 3600+7200+7200 |
Vertices | 7200 |
Vertex figure | Crossed isosceles trapezoidal pyramid, base edge lengths (1+√5)/2, √3, (√5–1)/2, √3; lateral edge lengths √2, √2, √(5+√5)/2, √(5+√5)/2 |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Ided–5–pip: 162° |
Ided–5/2–tigid: 144° | |
Grid–4–pip: | |
Ided–6–grid: 120° | |
Tigid–10–grid: 36° | |
Related polytopes | |
Army | Semi-uniform Grix, edge lengths (pentagonal prisms), (remaining edges) |
Regiment | Pirghi |
Conjugate | Great prismatohecatonicosidishecatonicosachoron |
Abstract & topological properties | |
Flag count | 230400 |
Euler characteristic | –1560 |
Orientable | Yes |
Properties | |
Symmetry | H,sub>4, order 14400 |
Convex | No |
Nature | Tame |
The small prismatohecatonicosidishecatonicosachoron, or siphidy, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 120 truncated great dodecahedra, 120 icosidodecadodecahedra, and 120 great rhombicosidodecahedra. 1 pentagonal prism, 1 truncated great dodecahedron, 1 icosidodecadodecahedron, and 2 great rhombicosidodecahedra join at each vertex.
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the prismatorhombated greeat hecatonicosachoron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 10: Prismatorhombates" (#374).
- Klitzing, Richard. "siphidy".