Small dispinosnub hexacosi prismatosnub pentishexacosichoron

Small dispinosnub hexacosi prismatosnub pentishexacosichoron
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sedansix paspox
Elements
Cells	600 small stellated dodecahedron, 600 snub disoctahedra, 2400 compound of two cubohemioctahedra, 600 compound of two small icosicosidodecahedra, 600 small rhombidodecahedra, 3600 pentagrammic prisms
Faces	14400 triangles, 32400 squares, 14400 pentagrams, 14400 hexagons, 4800 golden hexagrams, 3600 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	Gedansix paspox
Abstract & topological properties
Euler characteristic	33600
Orientable	No
Properties
Symmetry	H4+, order 7200
Convex	No
Nature	Wild

The small dispinosnub hexacosi prismatosnub pentishexacosichoron, or sedansix paspox, is a nonconvex uniform polychoron that consists of 600 small stellated dodecahedra, 1200 icosahedra (some of which lie in the same hyperplanes, forming 600 snub disoctahedra), 4800 cubohemioctahedra (forming 2400 compounds of two), 1200 small icosicosidodecahedra (forming 600 compounds of two), 600 small rhombidodecahedra, and 3600 pentagrammic prisms.

One small stellated dodecahedron, two icosahedra (two compounds), eight cubohemioctahedra (eight compounds), ten small icosicosidodecahedra (ten compounds), five small rhombidodecahedra, and five pentagrammic prisms join at each vertex.

It can be obtained as the blend of 5 small dipentary prismatohecatonicosihexacosihecatonicosachora and 5 small dipentary hecatonicosihexacositrishecatonicosachora. In the process, some of the cubohemioctahedron cells blend out.

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" (#1608).