# Small cubicuboctahedral prism

Small cubicuboctahedral prism Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSoccope
Coxeter diagramx x4/3o3x4*b (      )
Elements
Cells8 triangular prisms, 6 cubes, 6 octagonal prisms, 2 small cubicuboctahedra
Faces16 triangles, 12+24+24 squares, 12 octagons
Edges24+48+48
Vertices48
Vertex figureCrossed isosceles trapezoidal pyramid, edge lengths 1, 2+2, 2, 2+2 (base), 2 (legs)
Measures (edge length 1)
Circumradius$\sqrt{\frac{3+\sqrt2}{2}} ≈ 1.48563$ Hypervolume$2\frac{3+4\sqrt2}{3} ≈ 5.77214$ Dichoral anglesSocco–4–cube: 90°
Socco–3–trip: 90°
Socco–8–op: 90°
Cube–4–op: 90°
Trip–4–op: $\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561^\circ$ Height1
Central density2
Number of pieces80
Related polytopes
ArmySircope
RegimentSircope
DualSmall hexacronic icositetrahedral tegum
ConjugateGreat cubicuboctahedral prism
Abstract properties
Euler characteristic–6
Topological properties
OrientableYes
Properties
SymmetryB3×A1, order 96
ConvexNo
NatureTame

The small cubicuboctahedral prism or soccope is a prismatic uniform polychoron that consists of 2 small cubicuboctahedra, 6 cubes, 8 triangular prisms, and 6 octagonal prisms. Each vertex joins 1 small cubicuboctahedron, 1 triangular prism, 1 cube, and 2 octagonal prisms. As the name suggests, it is a prism based on the small cubicuboctahedron.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small rhombicuboctahedral prism.