Compound of five stellated truncated cubes

This uniform polyhedron compound is a composition of 5 stellated truncated cubes, formed by star-truncating each of the cubes in the compound of 5 cubes.

Cartesian coordinates

Cartesian coordinates for the vertices of this compound are all the cyclic permutations of

(±(2−√2), ±√2, ±(2−√2))

(±τ, ±(τ⁻¹−τ⁻¹√2), ±(2τ−1−τ√2))

(±1, ±(τ⁻²+τ⁻¹√2), ±(τ²−τ√2))

(±(1−√2), ±(−τ⁻²+√2), ±(τ²−√2))

(±(τ−τ√2), ±(−τ⁻¹), ±(2τ−1−τ⁻¹√2))

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

References

• Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society 79: 447–457, doi:10.1017/S0305004100052440, MR0397554 .