Compound of twelve pentagonal prisms

Compound of twelve pentagonal prisms
File: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:

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

References

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