# Quasitruncated cuboctahedral prism

Quasitruncated cuboctahedral prism
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymQuitcope
Coxeter diagramx x4/3x3x ()
Elements
Cells12 cubes, 8 hexagonal prisms, 6 octagrammic prisms, 2 quasitruncated cuboctahedra
Faces24+24+24+24 squares, 16 hexagons, 12 octagrams
Edges48+48+48+48
Vertices96
Vertex figureIrregular tetrahedron, edge lengths 2, 3, 2–2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{7-3\sqrt2}{2}} ≈ 1.17417}$
Hypervolume${\displaystyle 2\left(11-7\sqrt2\right) ≈ 2.20101}$
Dichoral anglesCube–4–stop: 135°
Quitco–8/3–stop: 90°
Quitco–6–hip: 90°
Quitco–4–cube: 90°
Hip–4–stop: ${\displaystyle \arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561^\circ}$
Cube–4–hip: ${\displaystyle \arccos\left(\frac{\sqrt6}{3}\right) ≈ 35.26439^\circ}$
Height1
Central density-1
Number of pieces150
Related polytopes
ArmySemi-uniform Gircope
RegimentQuitcope
DualGreat disdyakis dodecahedral tegum
ConjugateGreat rhombicuboctahedral prism
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryB3×A1, order 96
ConvexNo
NatureTame
Discovered by{{{discoverer}}}

The quasitruncated cuboctahedral prism, or quitcope, is a prismatic uniform polychoron that consists of 2 quasitruncated cuboctahedra, 6 octagrammic prisms, 8 hexagonal prisms, and 12 cubes. Each vertex joins one of each type of cell. As the name suggests, it is a prism based on the quasitruncated cuboctahedron.

The quasitruncated cuboctahedral prism can be vertex-inscribed into the great cubihexadecadisoctachoron.

## Vertex coordinates

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

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