Great hexacosihecatonicosidishecatonicosachoron |
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Rank | 4 |
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Type | Uniform |
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Notation |
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Bowers style acronym | Gixhidy |
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Coxeter diagram | x3o3o5x5/3*a () |
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Elements |
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Cells | 600 tetrahedra, 120 dodecahedra, 120 quasitruncated great stellated dodecahedra, 120 quasitruncated small stellated dodecahedra |
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Faces | 2400 triangles, 1440 pentagons, 1440 decagrams |
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Edges | 3600+3600 |
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Vertices | 2400 |
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Vertex figure | Triangular antipodium, edge lengths 1 (small base), (1+√5)/2 (large base), and √(5–√5)/2 (sides) |
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Measures (edge length 1) |
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Circumradius | |
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Hypervolume | |
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Dichoral angles | Doe–5–quit sissid: 144° |
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| Quit sissid–10/3–quit gissid: 108° |
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| Tet–3–quit gissid: |
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Number of external pieces | 8760 |
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Level of complexity | 43 |
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Related polytopes |
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Army | Semi-uniform Sidpixhi, edge lengths (dodecahedra), (tetrahedra) |
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Regiment | Gixhidy |
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Conjugate | Small hexacosihecatonicosidishecatonicosachoron |
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Abstract & topological properties |
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Flag count | 115200 |
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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 hexacosihecatonicosidishecatonicosachoron, or gixhidy, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, 120 quasitruncated great stellated dodecahedra, and 120 quasitruncated small stellated dodecahedra. 1 tetrahedron, 1 dodecahedron, 3 quasitruncated great stellated dodecahedra, and 3 quasitruncated small stellated dodecahedra join at each vertex.
The vertices of a great hexacosihecatonicosidishecatonicosachoron of edge length 1 are all permutations of:
along with the even permutations of:
The great hexacosihecatonicosidishecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the great hecatonicosafaceted hecatonicosihexacosihecatonicosachoron, great hexacosifaceted trishecatonicosachoron, great hecatonicosihecatonicosihexacosichoron, hecatonicosidishecatonicosachoron, great spinohexacosidishecatonicosachoron, and great spinohecatonicosidishecatonicosachoron.