Small diretrosnub prismatodisnub dishexacositetrishexacosichoron

Small diretrosnub prismatodisnub dishexacositetrishexacosichoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Saderspid sadixtux
Elements
Cells	600 great icosahedra, 600 compound of icosahedron and great dodecahedron, 2400 compound of two octahemioctahedra, 600 compound of two small dodecicosahedra, 600 small rhombicosidodecahedra, 6000 triangular prisms
Faces	38400 triangles, 18000 squares, 7200 pentagons, 14400 hexagons, 2400 golden hexagrams, 7200 decagons, 3600 compound of two hexagons
Edges	14400+2×21600
Vertices	7200
Measures (edge length 1)
Circumradius	${\sqrt {4+{\sqrt {5}}}}\approx 2.49721$
Related polytopes
Army	Semi-uniform Prahi
Regiment	Sadros daskydox
Conjugate	Gaderspid sadixtux
Abstract & topological properties
Euler characteristic	32400
Orientable	No
Properties
Symmetry	H4+, order 7200
Convex	No
Nature	Wild

The small diretrosnub prismatodisnub dishexacositetrishexacosichoron, or saderspid sadixtux, is a nonconvex uniform polychoron that consists of 600 great icosahedra, 600 icosahedra and 600 great dodecahedra (some of which lie in the same hyperplanes, forming 600 compounds of one of each), 4800 octahemioctahedra (forming 2400 compounds of two), 1200 small dodecicosahedra (forming 600 compounds of two), 600 small rhombicosidodecahedra, and 6000 triangular prisms.

One great icosahedron, one icosahedron and one great dodecahedron (two compounds), eight octahemioctahedra (eight compounds), ten small dodecicosahedra (ten compounds), five small rhombicosidodecahedra, and five triangular prisms join at each vertex.

It can be obtained as the blend of 5 small dipentary dishecatonicosihexacosihecatonicosachora and 5 small dipentary trishecatonicosiprismatohexacosichora.

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 28: Idcossids" (#1547).