Compound of twelve pentagonal prisms

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Short description: Polyhedral compound
Compound of twelve pentagonal prisms
UC35-12 pentagonal prisms.png
Type Uniform compound
Index UC35
Polyhedra 12 pentagonal prisms
Faces 24 pentagons, 60 squares
Edges 180
Vertices 60
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent 5-fold dihedral (D5)

This uniform polyhedron compound is a symmetric arrangement of 12 pentagonal 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 pentagonal prisms. In doing so, the vertices of the two enantiomorphs coincide, with the result that the full compound has two pentagonal prisms incident on each of its vertices.

Related polyhedra

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

Uniform great rhombicosidodecahedron.png
Nonconvex great rhombicosidodecahedron
Great dodecicosidodecahedron.png
Great dodecicosidodecahedron
Great rhombidodecahedron.png
Great rhombidodecahedron
Great truncated dodecahedron.png
Truncated great dodecahedron
UC34-6 pentagonal prisms.png
Compound of six pentagonal prisms
UC35-12 pentagonal prisms.png
Compound of twelve pentagonal prisms

References