Great skewverted hexacositrishecatonicosachoron |
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Rank | 4 |
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Type | Uniform |
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Notation |
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Bowers style acronym | Gik vixathi |
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Coxeter diagram | x3x3o3x5/3*a5/2*c () |
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Elements |
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Cells | 600 cuboctahedra, 120 small icosicosidodecahedra, 120 great dodecicosidodecahedra, 120 great quasitruncated icosidodecahedra |
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Faces | 2400+2400 triangles, 3600 squares, 1440 pentagrams, 2400 hexagons, 1440 decagrams |
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Edges | 7200+7200+7200 |
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Vertices | 7200 |
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Vertex figure | Skewed wedge, base edge lengths 1, 1, (√5–1)/2; lateral edge lengths √2, √3, √(5–√5)/2 |
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Measures (edge length 1) |
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Circumradius | |
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Hypervolume | |
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Dichoral angles | Gaddid–3–co: |
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| Gaddid–10/3–gaquatid: 144° |
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| Co–4–gaquatid: 135° |
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| Siid–6–gaquatid: 120° |
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| Gaddid–5/2–siid: 108° |
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| Siid–3–co: |
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Related polytopes |
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Army | Semi-uniform Grix, edge lengths (truncated icosahedra), (sides of pentagonal prisms) |
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Regiment | Gik vixathi |
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Conjugate | Small skewverted hexacositrishecatonicosachoron |
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Abstract & topological properties |
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Flag count | 259200 |
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Euler characteristic | –1680 |
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Orientable | Yes |
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Properties |
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Symmetry | H4, order 14400 |
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Convex | No |
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Nature | Tame |
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The great skewverted hexacositrishecatonicosachoron, or gik vixathi, is a nonconvex uniform polychoron that consists of 600 cuboctahedra, 120 small icosicosidodecahedra, 120 great dodecicosidodecahedra, and 120 great quasitruncated icosidodecahedra. 1 cuboctahedron, 1 small icosicosidodecahedron, 1 great dodecicosidodecahedron, and 2 great quasitruncated icosidodecahedra join at each vertex.
The vertices of a great skewverted hexacositrishecatonicosachoron of edge length 1 are given by all permutations of:
Plus all even permutations of:
The great skewverted hexacositrishecatonicosachoron is the colonel of a regiment of 15 members, including three other Wythoffians, namely the great skewverted ditrigonal hexacositrishecatonicosachoron, great skewverted ditrigonal prismatohexacosidishecatonicosachoron, and great skewverted dishexacosidishecatonicosachoron.