Prismatorhombated great grand hecatonicosachoron

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Prismatorhombated great grand hecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymPirgaghi
Coxeter diagramx5o5/2x3x ()
Elements
Cells
Faces
Edges3600+7200+7200
Vertices7200
Vertex figureIsosceles trapezoidal pyramid, base edge lengths (1+5)/2, 2, (5–1)/2, 2; lateral edge lengths 2, 2, 3, 3
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angleTiggy–6–hip: 150°
Pip–4–hip:
Raded–5–pip: 126°
Raded–4–hip:
Raded–5/2–tiggy: 108°
Related polytopes
ArmySemi-uniform Prix, edge lengths (triangular prisms), (remaining edges of truncated dodecahedra)
RegimentPirgaghi
ConjugatePrismatorhombated stellated hecatonicosachoron
Abstract & topological properties
Flag count230400
Euler characteristic–480
OrientableYes
Properties
SymmetryH4, order 14400
Flag orbits16
ConvexNo
NatureTame

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.

Vertex coordinates[edit | edit source]

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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Gallery[edit | edit source]

Related polychora[edit | edit source]

The prismatorhombated great grand hecatonicosachoron is the colonel of a 3-member regiment that also includes the great prismatohecatonicosihecatonicosihexacosichoron and the great rhombiprismic hecatonicosihexacosichoron.

External links[edit | edit source]