# Cuboctatruncated cuboctahedral prism

Cuboctatruncated cuboctahedral prism
Rank4
TypeUniform
SpaceSpherical
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${\displaystyle \sqrt2 ≈ 1.41421}$
Hypervolume10
Dichoral anglesHip–4–stop: ${\displaystyle \arccos\left(-\frac{\sqrt3}{3}\right) ≈ 125.26439^\circ}$
Cotco–8/3–stop: 90°
Cotco–6–hip: 90°
Cotco–8–op: 90°
Op–4–stop: 90°
Hip–4–op: ${\displaystyle \arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561^\circ}$
Height1
Central density4
Number of pieces64
Related polytopes
ArmySemi-uniform Gircope
RegimentCotcope
ConjugateCuboctatruncated cuboctahedral prism
Abstract properties
Euler characteristic–6
Topological properties
OrientableYes
Properties
SymmetryB3×A1, order 96
ConvexNo
NatureTame
Discovered by{{{discoverer}}}

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.

## Vertex coordinates

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

• ${\displaystyle \left(±\frac{1+\sqrt2}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12,\,±\frac12\right).}$