Compound of two snub cubes

This uniform polyhedron compound is a composition of the 2 enantiomers of the snub cube. As a holosnub, it is represented by Schläfli symbol &beta;r{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
 * (±1, ±ξ, ±1/ξ)

where ξ is the real solution to
 * $$\xi^3+\xi^2+\xi=1, \,$$

which can be written
 * $$\xi = \frac{1}{3}\left(\sqrt[3]{17+3\sqrt{33}} - \sqrt[3]{-17+3\sqrt{33}} - 1\right)$$

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:
 * (±1, ±t, ±$1⁄t$)

Truncated cuboctahedron
This compound can be seen as the union of the two chiral alternations of a truncated cuboctahedron:
 * Snubcubes in grCO.svgTRIBONACCI.jpg