The great cubicuboctahedron is the uniform polyhedron with Maeder index 14 (Maeder 1997), Wenninger index 77 (Wenninger 1989), Coxeter
index 50 (Coxeter et al. 1954), and Har'El index 19 (Har'El 1993). It has
Wythoff symbol 
and its faces are 
. It is a faceted
version of the cube.
The great cubicuboctahedron is implemented in the Wolfram Language as UniformPolyhedron[77],
UniformPolyhedron["SmallDitrigonalIcosidodecahedron"],
UniformPolyhedron[
"Coxeter",
50
],
UniformPolyhedron[
"Kaleido",
19
],
UniformPolyhedron[
"Uniform",
14
],
or UniformPolyhedron[
"Wenninger",
77
].
It is also implemented in the Wolfram
Language as PolyhedronData["GreatCubicuboctahedron"].
The skeleton of the great cubicuboctahedron is the small rhombicuboctahedral graph, illustrated above.
The circumradius of a great cubicuboctahedron with unit edge lengths is
 |
The convex hull of the great cubicuboctahedron is the Archimedean truncated cube, whose dual is the small triakis octahedron, so the dual of the great cubicuboctahedron (i.e., the great hexacronic icositetrahedron) is one of the stellations of the small triakis octahedron (Wenninger 1983, p. 57).
Its dual polyhedron is the great hexacronic icositetrahedron.
