Dishecatonicosaquasitruncated dishecatonicosachoron |
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Rank | 4 |
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Type | Uniform |
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Notation |
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Bowers style acronym | Dahiquatady |
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Coxeter diagram | o5x3x5x5/3*b () |
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Elements |
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Cells | 120 quasitruncated small stellated dodecahedra, 120 truncated icosahedra, 120 icosidodecatruncated icosidodecahedra |
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Faces | 1440 pentagons, 2400 hexagons, 720 decagons, 1440 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+√5)/2 (1), √3 (2), √(5+√5)/2 (1), and √(5–√5)/2 (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 | Idtid–10/3–quit sissid: 144° |
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| Ti–5–quit sissid: 144° |
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| Idtid–10–idtid: 144° |
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| Idtid–6–ti: 120° |
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Number of external pieces | 13560 |
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Level of complexity | 65 |
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Related polytopes |
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Army | Semi-uniform Prahi, edge lengths (small rhombicosidodecahedra), 1 (sides of pentagonal prisms) |
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Regiment | Dahiquatady |
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Conjugate | Dishecatonicositruncated dishecatonicosachoron |
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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 | –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 dishecatonicosaquasitruncated dishecatonicosachoron, or dahiquatady, is a nonconvex uniform polychoron that consists of 120 quasitruncated small stellated dodecahedra, 120 truncated icosahedra, and 120 icosidodecatruncated icosidodecahedra. 1 quasitruncated small stellated dodecahedron, 1 truncated icosahedron, and 2 icosidodecatruncated icosidodecahedra join at each vertex.
The vertices of a dishecatonicosiquasitruncated dishecatonicosachoron of edge length 1 are given by all permutations of:
Plus all even permutations of: