Great rhombated hecatonicosachoron

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Great rhombated hecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGrahi
Coxeter diagramx5x3x3o ()
Elements
Cells1200 triangular prisms, 600 truncated tetrahedra, 120 great rhombicosidodecahedra
Faces2400 triangles, 3600 squares, 2400 hexagons, 720 decagons
Edges3600+3600+7200
Vertices7200
Vertex figureSphenoid edge lengths 1 (1), 2 (2), 3 (2), and (5+5)/2 (1)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTut–3–trip:
 Grid–4–trip:
 Grid–6–tut:
 Grid–10–grid: 144°
Central density1
Number of external pieces1920
Level of complexity12
Related polytopes
ArmyGrahi
RegimentGrahi
DualGreat sphenoidal heptachiliadiacosichoron
ConjugateGreat quasirhombated great grand stellated hecatonicosachoron
Abstract & topological properties
Flag count172800
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
ConvexYes
NatureTame

The great rhombated hecatonicosachoron, or grahi, also commonly called the cantitruncated 120-cell, is a convex uniform polychoron that consists of 1200 triangular prisms, 600 truncated tetrahedra, and 120 great rhombicosidodecahedra. 1 triangular prism, 1 truncated tetrahedron, and 2 great rhombicosidodecahedra join at each vertex. As one of its names suggests, it can be obtained by cantitruncating the hecatonicosachoron.

Vertex coordinates[edit | edit source]

The vertices of a great rhombated hecatonicosachoron of edge length 1 are given by all permutations of:

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plus all even permutations of:

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Semi-uniform variant[edit | edit source]

The great rhombated hecatonicosachoron has a semi-uniform variant of the form x5y3z3o that maintains its full symmetry. This variant uses 600 truncated tetrahedra of form y3z3o, 120 great rhombicosidodecahedra of form x5y3z, and 1200 triangular prisms of form x z3o as cells, with 3 edge lengths.

With edges of length a, b, and c (such that it forms a5b3c3o), its circumradius is given by .

External links[edit | edit source]