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Compound of two snub dodecahedra

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Compound of two snub dodecahedra
Type Uniform compound
Index UC69
Schläfli symbol βr{5,3}
Coxeter diagram
Polyhedra 2 snub dodecahedra
Faces 40+120 triangles, 24 pentagons
Edges 300
Vertices 120
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent chiral icosahedral (I)

This uniform polyhedron compound is a composition of the 2 enantiomers of the snub dodecahedron.

The vertex arrangement of this compound is shared by a convex nonuniform truncated icosidodecahedron, with rectangular faces, alongside irregular hexagons and decagons, each alternating two different edge lengths.

Together with its convex hull, it represents the snub dodecahedron-first projection of the nonuniform snub dodecahedral antiprism.

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.