This uniform polyhedron compound is a composition of the 2 enantiomers of the snub cube. As a holosnub, it is represented by Schläfli symbol βr{4,3} and Coxeter diagram. The vertex arrangement of this compound is shared by a convex nonuniform truncated cuboctahedron, having rectangular faces, alongside irregular hexagons and octagons, each alternating with two edge lengths. Together with its convex hull, it represents the snub cube-first projection of the nonuniform snub cubic antiprism.

Cartesian coordinates

Cartesian coordinates for the vertices are all the permutations of where ξ is the real solution to which can be written or approximately 0.543689. ξ is the reciprocal of the tribonacci constant. Equally, the tribonacci constant, t, just like the snub cube, can compute the coordinates as:

Truncated cuboctahedron

This compound can be seen as the union of the two chiral alternations of a truncated cuboctahedron: