Compound of twelve pentagrammic crossed antiprisms with rotational freedom

Compound of twelve pentagrammic crossed antiprisms with rotational freedom
Compound of twelve pentagrammic crossed antiprisms with rotational freedom
UC28-12 pentagrammic crossed antiprisms.png
Type Uniform compound
Index UC28
Polyhedra 12 pentagrammic crossed antiprisms
Faces 120 triangles, 24 pentagrams
Edges 240
Vertices 120
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent 10-fold improper rotation (S10)

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.

References

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


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