Compound of five small stellated dodecahedra

Compound of five small stellated dodecahedra
Type Uniform compound
Index UC51
Polyhedra 5 small stellated dodecahedra
Faces 60 pentagrams
Edges 150
Vertices 60
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent pyritohedral (Th)

This uniform polyhedron compound is a composition of 5 small stellated dodecahedra, in the same arrangement as in the compound of 5 icosahedra.

It is one of only five polyhedral compounds (along with the compound of six tetrahedra, the compound of two great dodecahedra, the compound of five great dodecahedra, and the compound of two small stellated dodecahedra) which is vertex-transitive and face-transitive but not edge-transitive.

References

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  • Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554.