Sphenoverted trishecatonicosachoron |
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Rank | 4 |
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Type | Uniform |
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Notation |
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Bowers style acronym | Wavathi |
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Coxeter diagram | o5x3o5/2x5/3*b () |
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Elements |
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Cells | 120 icosidodecahedra, 120 quasitruncated small stellated dodecahedra, 120 great dodecicosidodecahedra |
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Faces | 2400 triangles, 1440 pentagons, 720 pentagrams, 1440 decagrams |
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Edges | 3600+7200 |
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Vertices | 3600 |
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Vertex figure | Wedge, edge lengths (1+√5)/2 (two edges of base rectangle), 1 (remaining base edges), √(5–√5)/2 (side edges), and (√5–1)/2 (top edge) |
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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–5/2–gaddid: 144° |
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| Gaddid–10/3–quit sissid: 144° |
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| Id–5–quit sissid: 72° |
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| Gaddid–3–id: 60° |
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Number of external pieces | 7560 |
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Related polytopes |
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Army | Semi-uniform Srix, edge lengths (icosidodecahedra), (main triangles) |
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Regiment | Wavathi |
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Conjugate | Retrosphenoverted trishecatonicosachoron |
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Abstract & topological properties |
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Flag count | 129600 |
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Euler characteristic | –1560 |
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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 sphenoverted trishecatonicosachoron, or wavathi, is a nonconvex uniform polychoron that consists of 120 quasitruncated small stellated dodecahedra, 120 icosidodecahedra, and 120 great dodecicosidodecahedra. 1 icosidodecahedron, 2 quasitruncated small stellated dodecahedra, and 2 great dodecicosidodecahedra join at each vertex.
Coordinates for the vertices of a sphenoverted trishecatonicosachoron of edge length 1 are given by all permutations of:
together with all even permutations of:
The sphenoverted trishecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the quasirhombated great stellated hecatonicosachoron, great rhombic hecatonicosihecatonicosachoron, pseudorhombic hecatonicosihecatonicosachoron, grand quasirhombic hecatonicosihecatonicosachoron, small prismatohecatonicosintercepted dishecatonicosachoron, and great hecatonicosintercepted trishecatonicosachoron.