Compound of twelve pentagrammic crossed antiprisms with rotational freedom
This uniform polyhedron compound is a symmetric arrangement of 12 pentagrammic crossed antiprisms. It can be constructed by inscribing one pair of pentagrammic crossed antiprisms within a great icosahedron, in each of the six possible ways, and then rotating each by an equal and opposite angle θ. When θ is 36 degrees, the antiprisms coincide in pairs to yield (two superimposed copies of) the compound of six pentagrammic crossed antiprisms (without rotational freedom). This compound shares its vertices with the compound of twelve pentagonal antiprisms with rotational freedom. Compound of twelve