# Small cubicuboctahedron

Small cubicuboctahedron
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSocco
Coxeter diagramx4/3o3x4*a ()
Elements
Faces8 triangles, 6 squares, 6 octagons
Edges24+24
Vertices24
Vertex figureCrossed isosceles trapezoid, edge lengths 1, 2+2, 2, 2+2
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt{5+2\sqrt2}}{2} ≈ 1.39897}$
Volume${\displaystyle 2\frac{3+4\sqrt2}{3} ≈ 5.77124}$
Dihedral angles8–4: 90°
8–3: ${\displaystyle \arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.735616^\circ}$
Central density2
Number of external pieces62
Level of complexity9
Related polytopes
ArmySirco
RegimentSirco
DualSmall hexacronic icositetrahedron
ConjugateGreat cubicuboctahedron
Convex coreCube
Abstract & topological properties
Flag count192
Euler characteristic–4
OrientableYes
Genus3
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

The small cubicuboctahedron, or socco, is a uniform polyhedron. It consists of 8 triangles, 6 squares, and 6 octagons. One triangle, one square, and two octagons meet at each vertex. It also has 12 square pseudofaces.

It is a faceting of the small rhombicuboctahedron, using its 6 squares and 8 triangles, along with 6 new octagons.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the rhombicuboctahedron.

## Representations

A small cubicuboctahedron has the following Coxeter diagrams:

• x4/3o3x4*a
• x4o3ß (, as holosnub)

## Related polyhedra

The rhombihyperhombicosicosahedron is a uniform polyhedron compound composed of 5 small cubicuboctahedra.

o4/3o3o4*a truncations
Name OBSA CD diagram Picture
(degenerate, double cover of cube) x4/3o3o4*a ()
Great cubicuboctahedron gocco x4/3x3o4*a ()
(degenerate, oct+6(4)) o4/3x3o4*a ()
(degenerate, double cover of cho) o4/3x3x4*a ()
(degenerate, oct+6(4)) o4/3o3x4*a ()
Small cubicuboctahedron socco x4/3o3x4*a ()
Cuboctatruncated cuboctahedron cotco x4/3x3x4*a ()