Compound of ten octahedra

The compounds of ten octahedra UC₁₅ and UC₁₆ are two uniform polyhedron compounds. They are composed of a symmetric arrangement of 10 octahedra, considered as triangular antiprisms, aligned with the axes of three-fold rotational symmetry of an icosahedron. The two compounds differ in the orientation of their octahedra: each compound may be transformed into the other by rotating each octahedron by 60 degrees.
For UC15, the convex hull of this compound is a nonuniform rhombicosidodecahedron. For UC16, the convex hull would be a nonuniform truncated icosahedron.

Cartesian coordinates

Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
where φ = /2 is the golden ratio and s is either +1 or −1. Setting s = −1 gives UC₁₅, while s = +1 gives UC₁₆.