Great quasirhombated small stellated hecatonicosachoron |
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Rank | 4 |
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Type | Uniform |
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Notation |
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Bowers style acronym | Gaqrisashi |
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Coxeter diagram | x5/3x5x3o () |
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Elements |
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Cells | 1200 triangular prisms, 120 truncated dodecahedra, 120 quasitruncated dodecadodecahedra |
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Faces | 2400 triangles, 3600 squares, 1440 decagons, 720 decagrams |
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Edges | 3600+3600+7200 |
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Vertices | 7200 |
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Vertex figure | Sphenoid, edge lengths 1 (1), √2 (2), √(5+√5)/2 (2), and √(5–√5)/2 (1) |
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Measures (edge length 1) |
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Circumradius | |
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Hypervolume | |
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Dichoral angles | Quitdid–4–trip: |
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| Quitdid–10/3–quitdid: 144° |
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| Quitdid–10–tid: 36° |
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| Tid–3–trip: 30° |
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Number of external pieces | 20640 |
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Level of complexity | 89 |
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Related polytopes |
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Army | Semi-uniform Grahi, edge lengths (decagons), (triangles) |
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Regiment | Gaqrisashi |
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Conjugate | Great quasirhombated great grand hecatonicosachoron |
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Convex core | Hecatonicosachoron |
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Abstract & topological properties |
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Flag count | 172800 |
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Euler characteristic | –480 |
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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 quasirhombated small stellated hecatonicosachoron, or gaqrisashi, is a nonconvex uniform polychoron that consists of 1200 triangular prisms, 120 truncated dodecahedra, and 120 quasitruncated dodecadodecahedra. 1 triangular prism, 1 truncated dodecahedron, and 2 quasitruncated dodecadodecahedra join at each vertex. As the name suggests, it can be obtained by quasicantitruncating the small stellated hecatonicosachoron.
The vertices of a great quasirhombated small stellated hecatonicosachoron of edge length 1 are given by all permutations of:
plus all even permutations of: