Great prismatohexacosidishecatonicosachoron |
---|
|
Rank | 4 |
---|
Type | Uniform |
---|
Notation |
---|
Bowers style acronym | Gippixady |
---|
Coxeter diagram | x3x3o5/2x5/3*b () |
---|
Elements |
---|
Cells | 720 pentagrammic prisms, 600 truncated tetrahedra, 120 great dodecicosidodecahedra, 120 great quasitruncated icosidodecahedra |
---|
Faces | 2400 triangles, 3600 squares, 1440 pentagrams, 2400 hexagons, 1440 decagrams |
---|
Edges | 3600+7200+7200 |
---|
Vertices | 7200 |
---|
Vertex figure | Isosceles trapezoidal pyramid, base edge lengths 1, √(5–√5)/2, (√5–1)/2, √(5–√5)/2; lateral edge lengths √2, √2, √3, √3 |
---|
Measures (edge length 1) |
---|
Circumradius | |
---|
Hypervolume | |
---|
Dichoral angles | Gaddid–5/2–stip: 126° |
---|
| Gaquatid–4–stip: |
---|
| Gaddid–10/3–gaquatid: 108° |
---|
| Tut–6–gaquatid: |
---|
| Gaddid–3–tut: |
---|
Related polytopes |
---|
Army | Semi-uniform Prahi, edge lengths (small rhombicosidodecahedra), (sides of pentagonal prisms) |
---|
Regiment | Gippixady |
---|
Conjugate | Small prismatohexacosidishecatonicosachoron |
---|
Abstract & topological properties |
---|
Flag count | 230400 |
---|
Euler characteristic | –1080 |
---|
Orientable | Yes |
---|
Properties |
---|
Symmetry | H4, order 14400 |
---|
Convex | No |
---|
Nature | Tame |
---|
The great prismatohexacosidishecatonicosachoron, or gippixady, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 600 truncated tetrahedra, 120 great dodecicosidodecahedra, and 120 great quasitruncated icosidodecahedra. 1 pentagrammic prism, 1 truncated tetrahedron, 1 great dodecicosidodecahedron, and 2 great quasitruncated icosidodecahedra join at each vertex.
The vertices of a great prismatohexacosidishecatonicosachoron of edge length 1 are given by all permutations of:
Plus all even permutations of:
The great prismatohexacosidishecatonicosachoron is the colonel of a 3-member regiment that also includes the prismatoquasirhombated great grand stellated hecatonicosachoron and great rhombiprismic dishecatonicosachoron.