# Quasitruncated cuboctahedral prism

Quasitruncated cuboctahedral prism
Rank4
TypeUniform
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${\displaystyle {\sqrt {\frac {7-3{\sqrt {2}}}{2}}}\approx 1.17417}$
Hypervolume${\displaystyle 2\left(11-7{\sqrt {2}}\right)\approx 2.20101}$
Dichoral anglesCube–4–stop: 135°
Quitco–8/3–stop: 90°
Quitco–6–hip: 90°
Quitco–4–cube: 90°
Hip–4–stop: ${\displaystyle \arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }}$
Cube–4–hip: ${\displaystyle \arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }}$
Height1
Central density-1
Number of external pieces150
Related polytopes
ArmySemi-uniform Gircope, edge lengths ${\displaystyle {\sqrt {2}}-1}$ (octagons), ${\displaystyle 2-{\sqrt {2}}}$ (remaining base edges), 1 (sides)
RegimentQuitcope
DualGreat disdyakis dodecahedral tegum
ConjugateGreat rhombicuboctahedral prism
Abstract & topological properties
Flag count2304
Euler characteristic0
OrientableYes
Properties
SymmetryB3×A1, order 96
ConvexNo
NatureTame

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.

• ${\displaystyle \left(\pm {\frac {2{\sqrt {2}}-1}{2}},\,\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right).}$