Compound of twelve pentagrammic prisms

This uniform polyhedron compound is a symmetric arrangement of 12 pentagrammic prisms, aligned in pairs with the axes of fivefold rotational symmetry of a dodecahedron.

Compound of twelve pentagrammic prisms
TypeUniform compound
IndexUC37
Polyhedra12 pentagrammic prisms
Faces24 pentagrams, 60 squares
Edges180
Vertices60
Symmetry groupicosahedral (Ih)
Subgroup restricting to one constituent5-fold dihedral (D5)

It results from composing the two enantiomorphs of the compound of six pentagrammic prisms. In doing so, the vertices of the two enantiomorphs coincide, with the result that the full compound has two pentagrammic prisms incident on each of its vertices.

This compound shares its vertex arrangement with four uniform polyhedra as follows:


Rhombicosidodecahedron

Small dodecicosidodecahedron

Small rhombidodecahedron

Small stellated truncated dodecahedron

Compound of six pentagrammic prisms

Compound of twelve pentagrammic prisms

References

  • Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (03): 447–457, doi:10.1017/S0305004100052440, MR 0397554.
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