Small rhombated small stellated hecatonicosachoron

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Small rhombated small stellated hecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSirsashi
Coxeter diagramx5/2o5x3o ()
Elements
Cells1200 triangular prisms, 120 icosidodecahedra, 120 rhombidodecadodecahedra
Faces2400 triangles, 3600 squares, 1440 pentagons, 720 pentagrams
Edges3600+7200
Vertices3600
Vertex figureWedge, edge lengths (1+5)/2 (two edges of base rectangle), 1 (other 2 base edges), 2 (side edges), and (5–1)/2 (top edge)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesRaded–4–trip:
 Id–3–trip: 150°
 Raded–5–id: 144°
 Raded–5/2–raded: 144°
Related polytopes
ArmySemi-uniform Xhi, edge lengths (pentagons), (triangles)
RegimentSirsashi
ConjugateSmall rhombated great grand hecatonicosachoron
Abstract & topological properties
Flag count129600
Euler characteristic–480
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The small rhombated small stellated hecatonicosachoron, or sirsashi, is a nonconvex uniform polychoron that consists of 1200 triangular prisms, 120 icosidodecahedra, and 120 rhombidodecadodecahedra. 1 icosidodecahedron, 2 triangular prisms, and 2 rhombidodecadodecahedra join at each vertex. it can be obtained by cantellating the small stellated hecatonicosachoron.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a small rhombated small 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 small stellated hecatonicosachoron is the colonel of a regiment of 7 members. Its other members include the medial retrosphenoverted hecatonicosihexacosihecatonicosachoron, rhombic small hecatonicosihexacosichoron, pseudorhombic small hexacosihecatonicosachoron, grand rhombic small dishecatonicosachoron, small hexacosihecatonicosintercepted dishecatonicosachoron, and small hecatonicosintercepted prismatodishecatonicosachoron.

External links[edit | edit source]