# Quasirhombicuboctahedral prism

Quasirhombicuboctahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymQuercope
Coxeter diagramx x4/3o3x ()
Elements
Cells8 triangular prisms, 6+12 cubes, 2 quasirhombicuboctahedra
Faces16 triangles, 12+24+24+24 squares
Edges24+48+48
Vertices48
Vertex figureCrossed isosceles trapezoidal pyramid, edge lengths 1, 2, 2, 2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {3-{\sqrt {2}}}{2}}}\approx 0.89045}$
Hypervolume${\displaystyle 2{\frac {5{\sqrt {2}}-6}{3}}\approx 0.71404}$
Dichoral anglesQuerco–4–cube: 90°
Querco–3–trip: 90°
Cube–4–cube: 45°
Trip–4–cube: ${\displaystyle \arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }}$
Height1
Central density5
Number of external pieces490
Related polytopes
ArmySemi-uniform Ticcup, edge lengths ${\displaystyle {\sqrt {2}}-1}$ (base), 1 (sides)
RegimentGoccope
DualGreat deltoidal icositetrahedral tegum
ConjugateSmall rhombicuboctahedral prism
Abstract & topological properties
Flag count1536
Euler characteristic0
OrientableYes
Properties
SymmetryB3×A1, order 96
ConvexNo
NatureTame

The quasirhombicuboctahedral prism or quercope is a prismatic uniform polychoron that consists of 2 quasirhombicuboctahedra, 6+12 cubes, and 8 triangular prisms. Each vertex joins 1 quasirhombicuboctahedron, 1 triangular prism, and 3 cubes. As the name suggests, it is a prism based on the quasirhombicuboctahedron.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great cubicuboctahedral prism.