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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 .
Contents
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.
Cartesian coordinates
Cartesian coordinates for the vertices are all the permutations of
(±1, ±ξ, ±1/ξ)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:
(±1, ±t, ±1/t)Truncated cuboctahedron
This compound can be seen as the union of the two chiral alternations of a truncated cuboctahedron: