Small rhombated grand stellated hecatonicosachoron

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Small rhombated grand stellated hecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSirgashi
Coxeter diagramx5/2o5x5/2o ()
Elements
Cells720 pentagrammic prisms, 120 dodecadodecahedra, 120 rhombidodecadodecahedra
Faces3600 squares, 1440 pentagons, 720+1440 pentagrams
Edges3600+7200
Vertices3600
Vertex figureWedge, edge lengths (5–1)/2 (two edges of base rectangle and top edge), (1+5)/2 (other 2 base edges), and 2 (side edges)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesDid–5/2–stip: 126°
 Raded–4–stip:
 Raded–5–did: 108°
 Raded–5/2–raded: 72°
Related polytopes
ArmySrahi, edge length
RegimentSirgashi
ConjugateSmall rhombated great hecatonicosachoron
Abstract & topological properties
Flag count129600
Euler characteristic–960
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The small rhombated grand stellated hecatonicosachoron, or sirgashi, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 120 dodecadodecahedra, and 120 rhombidodecadodecahedra. 1 dodecadodecahedron, 2 pentagrammic prisms, and 2 rhombidodecadodecahedra join at each vertex. it can be obtained by cantellating the grand stellated hecatonicosachoron.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a small rhombated grand stellated hecatonicosachoron of edge length 1 are given by all permutations of:

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together with all even permutations of:

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Related polychora[edit | edit source]

The small rhombated grand stellated hecatonicosachoron is the colonel of a regiment with 7 members. Its other members include the great retrosphenoverted hecatonicosidishecatonicosachoron, rhombic great dishecatonicosachoron, pseudorhombic great hecatonicosihexacosichoron, grand rhombic great hecatonicosihexacosichoron, great hecatonicosihexacosintercepted dishecatonicosachoron, and great hexacosintercepted prismatodishecatonicosachoron.

External links[edit | edit source]