Prismatorhombated stellated hecatonicosachoron

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Prismatorhombated stellated hecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymPirshi
Coxeter diagramx5/2o5x3x ()
Elements
Cells720 pentagrammic prisms, 1200 hexagonal prisms, 120 truncated icosahedra, 120 rhombidodecadodecahedra
Faces3600+3600 squares, 1440 pentagons, 1440 pentagrams, 2400 hexagons
Edges3600+7200+7200
Vertices7200
Vertex figureIsosceles trapezoidal pyramid, base edge lengths (5–1)/2, 2, (1+5)/2, 2; lateral edge lengths 2, 2, 3, 3
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesStip–4–hip:
 Raded–5/2–stip: 162°
 Raded–4–hip:
 Ti–6–hip: 150°
 Raded–5–ti: 144°
Related polytopes
ArmySemi-uniform Grix, edge lengths (pentagons), (remaining edges of truncated icosahedra), 1 (sides of pentagonal prisms)
RegimentPirshi
ConjugatePrismatorhombated great grand hecatonicosachoron
Abstract & topological properties
Flag count230400
Euler characteristic–480
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The prismatorhombated stellated hecatonicosachoron, or pirshi, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 1200 hexagonal prisms, 120 truncated icosahedra, and 120 rhombidodecadodecahedra. 1 pentagrammic prism, 2 hexagonal prisms, 1 truncated icosahedron, and 1 rhombidodecadodecahedron join at each vertex. It can be obtained by runcitruncating the faceted hexacosichoron.

Vertex coordinates[edit | edit source]

The vertices of a prismatorhombated stellated hecatonicosachoron of edge length 1 are given by all permutations of:

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plus all even permutations of:

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Related polychora[edit | edit source]

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

External links[edit | edit source]