Great diretrosnub snub pentishexacosipentishecatonicosachoron

Great diretrosnub snub pentishexacosipentishecatonicosachoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gadros spoxphi
Elements
Cells	600 small retrosnub disoctahedra, 600 icosahedra, 2400 compound of two octahemioctahedra, 600 rhombicosahedra, 600 great rhombidodecahedra, 120 truncated chiricosahedra, 2400 truncated tetrahedra
Faces	33600 triangles, 18000 squares, 19200 hexagons, 4800 golden hexagrams, 3600 decagrams, 1200 compound of two hexagons
Edges	14400+2×21600
Vertices	7200
Measures (edge length 1)
Circumradius	${\sqrt {4-{\sqrt {5}}}}\approx 1.32813$
Related polytopes
Army	Semi-uniform Grix
Regiment	Gadros daskydox
Conjugate	Small diretrosnub snub pentishexacosipentishecatonicosachoron
Abstract & topological properties
Euler characteristic	25200
Orientable	No
Properties
Symmetry	H4+, order 7200
Convex	No
Nature	Wild

The great diretrosnub snub pentishexacosipentishecatonicosachoron, or gadros spoxphi, is a nonconvex uniform polychoron that consists of 1200 great icosahedra (falling into pairs in the same hyperplanes, forming 600 small retrosnub disoctahedra), 600 icosahedra, 4800 octahemioctahedra (forming 2400 compounds of two), 600 rhombicosahedra, 600 great rhombidodecahedra, and 3000 truncated tetrahedra (600 of which form 120 truncated chiricosahedra).

Two great icosahedra (two compounds), one icosahedron, eight octahemioctahedra (eight compounds), five rhombicosahedra, five great rhombidodecahedra, and five truncated tetrahedra (one compound and four single) join at each vertex.

It can be obtained as the blend of 5 great dipentary hecatonicosidishexacosichora and 5 great based dipentary hexacositetrishecatonicosachora. In the process, some of the octahemioctahedron cells blend out.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great diretrosnub disnub decahecatonicosadishexacosichoron.

External links

• Bowers, Jonathan. "Category 29: Dircospids" (#1713).