Compound of six pentagrammic crossed antiprisms

This uniform polyhedron compound is a symmetric arrangement of 6 pentagrammic crossed antiprisms. It can be constructed by inscribing within a great icosahedron one pentagrammic crossed antiprism in each of the six possible ways, and then rotating each by 36 degrees AbOUT its axis (that passes through the centres of the two opposite pentagonal faces). It shares its vertices with the compound of 6 pentagonal antiprisms.

Cartesian coordinates

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

(±(3−4τ⁻¹), 0, ±(4+3τ⁻¹))

(±(2+4τ⁻¹), ±τ⁻¹, ±(1+2τ⁻¹))

(±(2−τ⁻¹), ±1, ±(4−2τ⁻¹))

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

References

• John Skilling, Uniform Compounds of Uniform Polyhedra, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 79, pp. 447-457, 1976.