Compound of two small stellated dodecahedra

Compound of two small stellated dodecahedra
Type Uniform compound
Index UC50
Polyhedra 2 small stellated dodecahedra
Faces 24 pentagrams
Edges 60
Vertices 24
Symmetry group octahedral (Oh)
Subgroup restricting to one constituent pyritohedral (Th)

This uniform polyhedron compound is a composition of 2 small stellated dodecahedra, in the same arrangement as in the compound of 2 icosahedra.

3D model of a compound of two small stellated dodecahedra

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 five small stellated dodecahedra) which is vertex-transitive and face-transitive but not edge-transitive.

Its convex hull is a nonuniform truncated octahedron.

References

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