Cuboctatruncated cuboctahedral prism

Cuboctatruncated cuboctahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Cotcope
Coxeter diagram	x x4/3x3x4*b ()
Elements
Cells	8 hexagonal prisms, 6 octagonal prisms, 6 octagrammic prisms, 2 cuboctatruncated cuboctahedra
Faces	24+24+24 squares, 16 hexagons, 12 octagons, 12 octagrams
Edges	48+48+48+48
Vertices	96
Vertex figure	Irregular tetrahedron, edge lengths √3, √2+√2, √2–√2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt2 ≈ 1.41421$
Hypervolume	10
Dichoral angles	Hip–4–stop: $\arccos\left(-\frac{\sqrt3}{3}\right) ≈ 125.26439^\circ$
	Cotco–8/3–stop: 90°
	Cotco–6–hip: 90°
	Cotco–8–op: 90°
	Op–4–stop: 90°
	Hip–4–op: $\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561^\circ$
Height	1
Central density	4
Number of pieces	64
Related polytopes
Army	Semi-uniform Gircope
Regiment	Cotcope
Dual	Tetradyakis hexahedral tegum
Conjugate	Cuboctatruncated cuboctahedral prism
Abstract properties
Euler characteristic	–6
Topological properties
Orientable	Yes
Properties
Symmetry	B3×A1, order 96
Convex	No
Nature	Tame
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.

Cross-sections

Vertex coordinates

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

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#949).

• Klitzing, Richard. "cotcope".