Great prismatohexacosidishecatonicosachoron

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Great prismatohexacosidishecatonicosachoron
Rank4
TypeUniform
Notation
Bowers style acronymGippixady
Coxeter diagramx3x3o5/2x5/3*b ()
Elements
Cells720 pentagrammic prisms, 600 truncated tetrahedra, 120 great dodecicosidodecahedra, 120 great quasitruncated icosidodecahedra
Faces2400 triangles, 3600 squares, 1440 pentagrams, 2400 hexagons, 1440 decagrams
Edges3600+7200+7200
Vertices7200
Vertex figureIsosceles trapezoidal pyramid, base edge lengths 1, (5–5)/2, (5–1)/2, (5–5)/2; lateral edge lengths 2, 2, 3, 3
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGaddid–5/2–stip: 126°
 Gaquatid–4–stip:
 Gaddid–10/3–gaquatid: 108°
 Tut–6–gaquatid:
 Gaddid–3–tut:
Related polytopes
ArmySemi-uniform Prahi, edge lengths (small rhombicosidodecahedra), (sides of pentagonal prisms)
RegimentGippixady
ConjugateSmall prismatohexacosidishecatonicosachoron
Abstract & topological properties
Flag count230400
Euler characteristic–1080
OrientableYes
Properties
SymmetryH4, order 14400
ConvexNo
NatureTame

The great prismatohexacosidishecatonicosachoron, or gippixady, is a nonconvex uniform polychoron that consists of 720 pentagrammic prisms, 600 truncated tetrahedra, 120 great dodecicosidodecahedra, and 120 great quasitruncated icosidodecahedra. 1 pentagrammic prism, 1 truncated tetrahedron, 1 great dodecicosidodecahedron, and 2 great quasitruncated icosidodecahedra join at each vertex.

Vertex coordinates[edit | edit source]

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

Plus all even permutations of:

Related polychora[edit | edit source]

The great prismatohexacosidishecatonicosachoron is the colonel of a 3-member regiment that also includes the prismatoquasirhombated great grand stellated hecatonicosachoron and great rhombiprismic dishecatonicosachoron.

External links[edit | edit source]