# Great cubicuboctahedron

Great cubicuboctahedron Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGocco
Coxeter diagramx4/3x3o4*a (    )
Elements
Faces8 triangles, 6 squares, 6 octagrams
Edges24+24
Vertices24
Vertex figureIsosceles trapezoid, edge lengths 1, 2–2, 2, 2–2 Measures (edge length 1)
Circumradius$\frac{\sqrt{5-2\sqrt2}}{2} \approx 0.73681$ Volume$2\frac{4\sqrt2-3}{3} \approx 1.77124$ Dihedral angles8/3–3: $\arccos\left(-\frac{\sqrt3}{3}\right) \approx 125.26439^\circ$ 8/3–4: 90°
Central density4
Number of external pieces62
Level of complexity13
Related polytopes
ArmyTic
RegimentGocco
DualGreat hexacronic icositetrahedron
ConjugateSmall cubicuboctahedron
Convex coreCube
Abstract & topological properties
Flag count192
Euler characteristic-4
OrientableYes
Genus3
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

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

## Vertex coordinates

A small rhombicuboctahedron of edge length 1 has vertex coordinates given by all permutations of:

• $\left(±\frac{\sqrt2-1}{2},\,±\frac12,\,±\frac12\right).$ ## Related polyhedra

The great cubicuboctahedron is the colonel of a three-member regiment that also includes the quasirhombicuboctahedron and the great rhombihexahedron.

The rhombiquasihyperhombicosicosahedron is a uniform polyhedron compound composed of 5 great 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 (   )