# Small cubicuboctahedral prism

Small cubicuboctahedral prism
Rank4
TypeUniform
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${\displaystyle {\sqrt {\frac {3+{\sqrt {2}}}{2}}}\approx 1.48563}$
Hypervolume${\displaystyle 2{\frac {3+4{\sqrt {2}}}{3}}\approx 5.77214}$
Dichoral anglesSocco–4–cube: 90°
Socco–3–trip: 90°
Socco–8–op: 90°
Cube–4–op: 90°
Trip–4–op: ${\displaystyle \arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }}$
Height1
Central density2
Number of external pieces80
Related polytopes
ArmySircope
RegimentSircope
DualSmall hexacronic icositetrahedral tegum
ConjugateGreat cubicuboctahedral prism
Abstract & topological properties
Flag count1536
Euler characteristic–6
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.