Great ditrigonal hecatonicosiprismatodishecatonicosachoron |
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Rank | 4 |
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Type | Uniform |
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Notation |
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Bowers style acronym | Gid thipady |
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Coxeter diagram | x5x3o5x5/3*b () |
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Elements |
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Cells | 720 pentagonal prisms, 120 truncated dodecahedra, 120 great ditrigonal dodecicosidodecahedra, 120 quasitruncated dodecadodecahedra |
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Faces | 2400 triangles, 3600 squares, 1440 pentagons, 1440 decagons, 1440 decagrams |
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Edges | 3600+7200+7200 |
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Vertices | 7200 |
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Vertex figure | Isosceles trapezoidal pyramid, base edge lengths 1, √(5–√5)/2, (1+√5)/2, √(5–√5)/2; lateral edge lengths √2, √2, √(5+√5)/2, √(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 | Gidditdid–5–pip: 162° |
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| Quitdid–4–pip: |
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| Gidditdid–10/3–quitdid: 144° |
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| Tid–10–quitdid: 144° |
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| Gidditdid–3–tid: 120° |
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Related polytopes |
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Army | Semi-uniform Prix, edge lengths (truncated dodecahedra), (bases of triangular prisms) |
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Regiment | Gid thipady |
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Conjugate | Small ditrigonal hecatonicosiprismatodishecatonicosachoron |
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Abstract & topological properties |
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Flag count | 230400 |
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Euler characteristic | –1560 |
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Orientable | Yes |
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Properties |
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Symmetry | [Hecatonicosachoric symmetry |
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Convex | No |
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Nature | Tame |
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The great ditrigonal hecatonicosiprismatodishecatonicosachoron, or gid thipady, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 120 truncated dodecahedra, 120 great ditrigonal dodecicosidodecahedra, and 120 quasitruncated dodecadodecahedra. 1 pentagonal prism, 1 truncated dodecahedron, 1 great ditrigonal dodecicosidodecahedron, and 2 quasitruncated dodecadodecahedra join at each vertex.
The vertices of a great ditrigonal hecatonicosiprismatodishecatonicosachoron of edge length 1 are given by all permutations of:
Plus all even permutations of:
The great ditrigonal hecatonicosiprismatodishecatonicosachoron is the colonel of a 3-member regiment that also includes the great hecatonicosiprismatodishecatonicosachoron and great hecatonicosihecatonicosihecatonicosachoron.