# Quasirhombicuboctahedral prism

Quasirhombicuboctahedral prism Rank4
TypeUniform
SpaceSpherical
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$\sqrt{\frac{3-\sqrt2}{2}} ≈ 0.89045$ Hypervolume$2\frac{5\sqrt2-6}{3} ≈ 0.71404$ Dichoral anglesQuerco–4–cube: 90°
Querco–3–trip: 90°
Cube–4–cube: 45°
Trip–4–cube: $\arccos\left(\frac{\sqrt6}{3}\right) ≈ 35.26439^\circ$ Height1
Central density5
Number of pieces490
Related polytopes
ArmySemi-uniform Ticcup
RegimentGoccope
DualGreat deltoidal icositetrahedral tegum
ConjugateSmall rhombicuboctahedral prism
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryB3×A1, order 96
ConvexNo
NatureTame
Discovered by{{{discoverer}}}

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.