Cishemiblended disnub triacontadiadisoctachoron

The cishemiblended disnub triacontadiadisoctachoron, or chebadestado, is a nonconvex uniform polychoron that consists of 8 great icosahedra, 8 icosahedra, 192 tetrahedra, 96+32 octahedra, 32+32+32 tetrahemihexahedra, 16 cuboctahedra, and 32 cubohemioctahedra. One great icosahedron, one icosahedron, eight tetrahedra, eight octahedra, six tetrahemihexahedra, two cuboctahedra, and four cubohemioctahedra join at each vertex.

Cishemiblended disnub triacontadiadisoctachoron
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Chebadestado
Elements
Cells	8 great icosahedra, 8 icosahedra, 192 tetrahedra, 96+32 octahedra, 32+32+32 tetrahemihexahedra, 16 cuboctahedra, 32 cubohemioctahedra
Faces	1312 triangles, 288 squares, 64 hexagons
Edges	288+384+96+48
Vertices	96
Measures (edge length 1)
Circumradius	1
Related polytopes
Army	Sadi
Regiment	Disdi
Conjugate	None
Abstract & topological properties
Euler characteristic	496
Orientable	No
Properties
Symmetry	D4+, order 96
Convex	No

It can be obtained as the blend of a snub hexecontatetrasnub-snub disoctachoron and 4 hexadecaocta-hemihexadecintercepted hemioctachora. In the process, some of the octahedron cells blend out.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the disnub disicositetrachoron.

Related polychora

The blend components and facet counts of the cishemiblended disnub triacontadiadisoctachoron are the same as those of three other idtessids, differing only in orientation. Those are the:

• hemicisblended disnub triacontadiadisoctachoron,
• hemitransblended disnub triacontadiadisoctachoron,
• transhemiblended disnub triacontadiadisoctachoron.

External links

• Bowers, Jonathan. "Category 30: Idtessids" (#1889).