Prismatorhombated great grand 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 | Pirgaghi |
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Coxeter diagram | x5o5/2x3x () |
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Elements |
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Cells | |
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Faces | |
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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)/2, √2, (√5–1)/2, √2; lateral edge lengths √2, √2, √3, √3 |
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Measures (edge length 1) |
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Circumradius | |
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Hypervolume | |
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Dichoral angle | Tiggy–6–hip: 150° Pip–4–hip: Raded–5–pip: 126° Raded–4–hip: Raded–5/2–tiggy: 108° |
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Related polytopes |
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Army | Semi-uniform Prix, edge lengths (triangular prisms), (remaining edges of truncated dodecahedra) |
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Regiment | Pirgaghi |
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Conjugate | Prismatorhombated stellated hecatonicosachoron |
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Abstract & topological properties |
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Flag count | 230400 |
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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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Flag orbits | 16 |
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Convex | No |
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Nature | Tame |
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The prismatorhombated great grand hecatonicosachoron, or pirgaghi, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 1200 hexagonal prisms, 120 truncated great icosahedra, and 120 rhombidodecadodecahedra. 1 pentagonal prism, 2 hexagonal prisms, 1 truncated great icosahedron, and 1 rhombidodecadodecahedron join at each vertex. It can be obtained by runcitruncating the great faceted hexacosichoron.
The vertices of a prismatorhombated great grand hecatonicosachoron of edge length 1 are given by all permutations of:
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plus all even permutations of:
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The prismatorhombated great grand hecatonicosachoron is the colonel of a 3-member regiment that also includes the great prismatohecatonicosihecatonicosihexacosichoron and the great rhombiprismic hecatonicosihexacosichoron.
truncations |
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Name | OBSA | Schläfli symbol | CD diagram | Image |
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Great grand hecatonicosachoron | gaghi | {5,5/2,3} | | |
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Rectified great grand hecatonicosachoron | ragaghi | r{5,5/2,3} | | |
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Rectified great faceted hexacosichoron | rigfix | r{3,5/2,5} | | |
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Great faceted hexacosichoron | gofix | {3,5/2,5} | | |
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Truncated great grand hecatonicosachoron | tigaghi | t{5,5/2,3} | | |
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Small rhombated great grand hecatonicosachoron | sirgaghi | rr{5,5/2,3} | | |
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Quasiprismatodishecatonicosachoron | quipdohi | t0,3{5,5/2,3} | | |
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(degenerate) | | 2t{5,5/2,3} | | |
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(degenerate) | | rr{3,5/2,5} | | |
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Truncated great faceted hexacosichoron | tigfix | t{3,5/2,5} | | |
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(degenerate) | | t0,1,2{5,5/2,3} | | |
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(degenerate) | | t0,1,3{5,5/2,3} | | |
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Prismatorhombated great grand hecatonicosachoron | pirgaghi | t0,2,3{5,5/2,3} | | |
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(degenerate) | | t1,2,3{5,5/2,3} | | |
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(degenerate) | | t0,1,2,3{5,5/2,3} | | |
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