Small prismatohecatonicosidishecatonicosachoron

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Small prismatohecatonicosidishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSiphidy
Coxeter diagramx5x3x5o5/3*b ()
Elements
Cells720 pentagonal prisms, 120 truncated great dodecahedra, 120 icosidodecadodecahedra, 120 great rhombicosidodecahedra
Faces3600 squares, 1440 pentagons, 1440 pentagrams, 2400 hexagons, 1440 decagons
Edges3600+7200+7200
Vertices7200
Vertex figureCrossed isosceles trapezoidal pyramid, base edge lengths (1+5)/2, 3, (5–1)/2, 3; lateral edge lengths 2, 2, (5+5)/2, (5+5)/2
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesIded–5–pip: 162°
 Ided–5/2–tigid: 144°
 Grid–4–pip:
 Ided–6–grid: 120°
 Tigid–10–grid: 36°
Related polytopes
ArmySemi-uniform Grix, edge lengths (pentagonal prisms), (remaining edges)
RegimentPirghi
ConjugateGreat prismatohecatonicosidishecatonicosachoron
Abstract & topological properties
Flag count230400
Euler characteristic–1560
OrientableYes
Properties
SymmetryH,sub>4, order 14400
ConvexNo
NatureTame

The small prismatohecatonicosidishecatonicosachoron, or siphidy, is a nonconvex uniform polychoron that consists of 720 pentagonal prisms, 120 truncated great dodecahedra, 120 icosidodecadodecahedra, and 120 great rhombicosidodecahedra. 1 pentagonal prism, 1 truncated great dodecahedron, 1 icosidodecadodecahedron, and 2 great rhombicosidodecahedra join at each vertex.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the prismatorhombated greeat hecatonicosachoron.

External links[edit | edit source]