Compound of twelve pentagrammic prisms

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Compound of twelve pentagrammic prisms
UC37-12 pentagrammic prisms.png
Type Uniform compound
IndexUC37
Polyhedra12 pentagrammic prisms
Faces24 pentagrams, 60 squares
Edges180
Vertices60
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent5-fold dihedral (D5)

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.

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:

Small rhombicosidodecahedron.png
Rhombicosidodecahedron
Small dodecicosidodecahedron.png
Small dodecicosidodecahedron
Small rhombidodecahedron.png
Small rhombidodecahedron
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Small stellated truncated dodecahedron
UC36-6 pentagrammic prisms.png
Compound of six pentagrammic prisms
UC37-12 pentagrammic prisms.png
Compound of twelve pentagrammic prisms

References