Great skewverted hexacositrishecatonicosachoron

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Great skewverted hexacositrishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGik vixathi
Coxeter diagramx3x3o3x5/3*a5/2*c ()
Elements
Cells600 cuboctahedra, 120 small icosicosidodecahedra, 120 great dodecicosidodecahedra, 120 great quasitruncated icosidodecahedra
Faces2400+2400 triangles, 3600 squares, 1440 pentagrams, 2400 hexagons, 1440 decagrams
Edges7200+7200+7200
Vertices7200
Vertex figureSkewed wedge, base edge lengths 1, 1, (5–1)/2; lateral edge lengths 2, 3, (5–5)/2
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGaddid–3–co:
 Gaddid–10/3–gaquatid: 144°
 Co–4–gaquatid: 135°
 Siid–6–gaquatid: 120°
 Gaddid–5/2–siid: 108°
 Siid–3–co:
Related polytopes
ArmySemi-uniform Grix, edge lengths (truncated icosahedra), (sides of pentagonal prisms)
RegimentGik vixathi
ConjugateSmall skewverted hexacositrishecatonicosachoron
Abstract & topological properties
Flag count259200
Euler characteristic–1680
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The great skewverted hexacositrishecatonicosachoron, or gik vixathi, is a nonconvex uniform polychoron that consists of 600 cuboctahedra, 120 small icosicosidodecahedra, 120 great dodecicosidodecahedra, and 120 great quasitruncated icosidodecahedra. 1 cuboctahedron, 1 small icosicosidodecahedron, 1 great dodecicosidodecahedron, and 2 great quasitruncated icosidodecahedra join at each vertex.

Vertex coordinates[edit | edit source]

The vertices of a great skewverted hexacositrishecatonicosachoron of edge length 1 are given by all permutations of:

Plus all even permutations of:

Related polychora[edit | edit source]

The great skewverted hexacositrishecatonicosachoron is the colonel of a regiment of 15 members, including three other Wythoffians, namely the great skewverted ditrigonal hexacositrishecatonicosachoron, great skewverted ditrigonal prismatohexacosidishecatonicosachoron, and great skewverted dishexacosidishecatonicosachoron.

External links[edit | edit source]