Grand prismatotrishecatonicosachoron
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Grand prismatotrishecatonicosachoron | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Gapthi |
Coxeter diagram | x5/3x3/2o5x5*b () |
Elements | |
Cells | 720 pentagonal prisms, 120 quasitruncated great stellated dodecahedra, 120 small dodecicosidodecahedra, 120 quasitruncated dodecadodecahedra |
Faces | 2400 triangles, 3600 squares, 1440 pentagons, 1440 decagons, 1440 decagrams |
Edges | 3600+7200+7200 |
Vertices | 7200 |
Vertex figure | Crossed 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 |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Quitdid–4–pip: |
Saddid–10–quitdid: 72° | |
Saddid–3–quit gissid: 60° | |
Saddid–5–pip: 54° | |
Quit gissid–10/3–quitdid: 36° | |
Related polytopes | |
Army | Semi-uniform Prahi |
Regiment | Quippirghi |
Conjugate | Medial prismatotrishecatonicosachoron |
Abstract & topological properties | |
Euler characteristic | –1560 |
Orientable | Yes |
Properties | |
Symmetry | H4, order 14400 |
Convex | No |
Nature | Tame |
The grand prismatotrishecatonicosachoron, or gapthi, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 120 quasitruncated great stellated dodecahedra, 120 small dodecicosidodecahedra, and 120 quasitruncated dodecadodecahedra. 1 pentagonal prism, 1 quasitruncated great stellated dodecahedron, 1 small dodecicosidodecahedron, and 2 quasitruncated dodecadodecahedra join at each vertex.
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the quasiprismatorhombated grand hecatonicosachoron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 10: Prismatorhombates" (#389).
- Klitzing, Richard. "gapthi".