Great diretrosnub dishexacositetrishexacosichoron

Great diretrosnub dishexacositetrishexacosichoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gadrosid xutix
Elements
Cells	600 small retrosnub disoctahedra, 600 icosahedra, 2400 compound of two octahemioctahedra, 600 great dodecicosahedra, 600 great dodecicosidodecahedra, 600 truncated great icosahedra
Faces	33600 triangles, 7200 pentagrams, 19200 hexagons, 4800 golden hexagrams, 7200 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 dishexacositetrishexacosichoron
Abstract & topological properties
Euler characteristic	20400
Orientable	No
Properties
Symmetry	H4+, order 7200
Convex	No
Nature	Wild

The great diretrosnub dishexacositetrishexacosichoron, or gadrosid xutix, 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 great dodecicosahedra, 600 great dodecicosidodecahedra, and 600 truncated great icosahedra.

Two great icosahedra (two compounds), one icosahedron, eight octahemioctahedra (eight compounds), five great dodecicosahedra, five great dodecicosidodecahedra, and five truncated great icosahedra join at each vertex.

It can be obtained as the blend of 5 great dipentary dishecatonicosihexacosihecatonicosachora and 5 great invertidipentary hecatonicosihexacosidishecatonicosachora. 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" (#1710).