# Great cubicuboctahedron

(Redirected from Gocco)
Great cubicuboctahedron
Rank3
TypeUniform
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${\displaystyle {\frac {\sqrt {5-2{\sqrt {2}}}}{2}}\approx 0.73681}$
Volume${\displaystyle 2{\frac {4{\sqrt {2}}-3}{3}}\approx 1.77124}$
Dihedral angles8/3–3: ${\displaystyle \arccos \left(-{\frac {\sqrt {3}}{3}}\right)\approx 125.26439^{\circ }}$
8/3–4: 90°
Central density4
Number of external pieces62
Level of complexity13
Related polytopes
ArmyTic, edge length ${\displaystyle {\sqrt {2}}-1}$
RegimentGocco
DualGreat hexacronic icositetrahedron
ConjugateSmall cubicuboctahedron
Convex coreCube
Abstract & topological properties
Flag count192
Euler characteristic-4
OrientableYes
Genus3
Properties
SymmetryB3, order 48
Flag orbits4
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 great cubicuboctahedron of edge length 1 has vertex coordinates given by all permutations of:

• ${\displaystyle \left(\pm {\frac {{\sqrt {2}}-1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right).}$

## 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 ()