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Compound of five great dodecahedra

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Compound of five great dodecahedra
Type Uniform compound
Index UC49
Polyhedra 5 great dodecahedra
Faces 60 pentagons
Edges 150
Vertices 60
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent pyritohedral (Th)

This uniform polyhedron compound is a composition of 5 great 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 two small stellated dodecahedra, and the compound of five 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.