Small rhombated hecatonicosachoron

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Small rhombated hecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymSrahi
Coxeter diagramx5o3x3o ()
Elements
Cells600 octahedra, 1200 triangular prisms, 120 small rhombicosidodecahedra
Faces2400+2400 triangles, 3600 squares, 720 pentagons
Edges3600+7200
Vertices3600
Vertex figureSquare wedge, edge lengths 1 (base square), 2 (side edges), and (1+5)/2 (top edge)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesOct–3–trip:
 Srid–4–trip:
 Srid–3–oct:
 Srid–5–srid: 144°
Central density1
Number of external pieces1920
Level of complexity9
Related polytopes
ArmySrahi
RegimentSrahi
DualGreat notched trischiliahexacosichoron
ConjugateQuasirhombated great grand stellated hecatonicosachoron
Abstract & topological properties
Flag count129600
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
ConvexYes
NatureTame

The small rhombated hecatonicosachoron, or srahi, also commonly called the cantellated 120-cell, is a convex uniform polychoron that consists of 600 regular octahedra, 1200 triangular prisms, and 120 small rhombicosidodecahedra. 1 octahedron, 2 triangular prisms, and 2 small rhombicosidodecahedra join at each vertex. As one of its names suggests, it can be obtained by cantellating the hecatonicosachoron.

Vertex coordinates[edit | edit source]

Coordinates for the vertices of a small rhombated 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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  • .

Semi-uniform variant[edit | edit source]

The small rhombated hecatonicosachoron has a semi-uniform variant of the form x5o3y3o that maintains its full symmetry. This variant uses 600 octahedra of size y, 120 semi-uniform small rhombicosidodecahedra of form x5o3y, and 1200 triangular prisms of form x y3o as cells, with 2 edge lengths.

With edges of length a (surrounded by two small rhombicosidodecahedra) and b (of octahedra), its circumradius is given by .

Related polychora[edit | edit source]

The small rhombated hecatonicosachoron is the colonel of a seven-member regiment. Its other members include the small retrosphenoverted hexacosidishecatonicosachoron, small rhombic dishecatonicosachoron, small pseudorhombic prismatohecatonicosachoron, grand rhombic prismatohecatonicosachoron, prismatohecatonicosintercepted hexacosihecatonicosachoron, and prismatointercepted prismatohexacosihecatonicosachoron.

The segmentochoron small rhombicosidodecahedron atop truncated dodecahedron can be obtained as a cap of the small rhombated hecatonicosachoron. Another possible cap is the pentagonal pucofastegium, viewed as a cap from a pentagonal face.

External links[edit | edit source]