Cuboctatruncated cuboctahedral prism

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Cuboctatruncated cuboctahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymCotcope
Coxeter diagramx x4/3x3x4*b ()
Elements
Cells8 hexagonal prisms, 6 octagonal prisms, 6 octagrammic prisms, 2 cuboctatruncated cuboctahedra
Faces24+24+24 squares, 16 hexagons, 12 octagons, 12 octagrams
Edges48+48+48+48
Vertices96
Vertex figureIrregular tetrahedron, edge lengths 3, 2+2, 2–2 (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume10
Dichoral anglesHip–4–stop:
 Cotco–8/3–stop: 90°
 Cotco–6–hip: 90°
 Cotco–8–op: 90°
 Op–4–stop: 90°
 Hip–4–op:
Height1
Central density4
Number of external pieces64
Related polytopes
ArmySemi-uniform Gircope, edge lengths (octagons), 1 (remaining edges)
RegimentCotcope
DualTetradyakis hexahedral tegum
ConjugateCuboctatruncated cuboctahedral prism
Abstract & topological properties
Flag count2304
Euler characteristic–6
OrientableYes
Properties
SymmetryB3×A1, order 96
ConvexNo
NatureTame

The cuboctatruncated cuboctahedral prism, or cotcope, is a prismatic uniform polychoron that consists of 2 cuboctatruncated cuboctahedra, 6 octagrammic prisms, 6 octagonal prisms, and 8 hexagonal prisms,. Each vertex joins one of each type of cell. As the name suggests, it is a prism based on the cuboctatruncated cuboctahedron.

The cuboctatruncated cuboctahedral prism can be vertex-inscribed into the small skewverted prismatohexadecadisoctachoron and the antifrustary distetracontoctachoron.

Cross-sections[edit | edit source]

Card with cell counts, vertex figure, and cross-sections.


Vertex coordinates[edit | edit source]

The vertices of a cuboctatruncated cuboctahedral prism of edge length 1 are given by all permutations of the first three coordinates of:

External links[edit | edit source]