Compound of twelve pentagonal prisms
Type	Uniform compound Uniform polyhedron compound A uniform polyhedron compound is a polyhedral compound whose constituents are identical uniform polyhedra, in an arrangement that is also uniform: the symmetry group of the compound acts transitively on the compound's vertices.The uniform polyhedron compounds were first enumerated by John Skilling...
Index	UC35
Polyhedra	12 pentagonal prism Pentagonal prism In geometry, the pentagonal prism is a prism with a pentagonal base. It is a type of heptahedron with 7 faces, 15 edges, and 10 vertices.- As a semiregular polyhedron :... s
Faces	24 pentagons, 60 squares Square (geometry) In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...
Edges	180
Vertices	60
Symmetry group Symmetry group The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...	icosahedral Icosahedral symmetry A regular icosahedron has 60 rotational symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation...  (Ih)
Subgroup Subgroup In group theory, given a group G under a binary operation *, a subset H of G is called a subgroup of G if H also forms a group under the operation *. More precisely, H is a subgroup of G if the restriction of * to H x H is a group operation on H...  restricting to one constituent	5-fold dihedral Dihedral symmetry in three dimensions This article deals with three infinite sequences of point groups in three dimensions which have a symmetry group that as abstract group is a dihedral group Dihn .See also point groups in two dimensions.Chiral:...  (D5)

This uniform polyhedron compound

Uniform polyhedron compound

A uniform polyhedron compound is a polyhedral compound whose constituents are identical uniform polyhedra, in an arrangement that is also uniform: the symmetry group of the compound acts transitively on the compound's vertices.The uniform polyhedron compounds were first enumerated by John Skilling...

 is a symmetric arrangement of 12 pentagonal prism

Pentagonal prism

In geometry, the pentagonal prism is a prism with a pentagonal base. It is a type of heptahedron with 7 faces, 15 edges, and 10 vertices.- As a semiregular polyhedron :...

s, aligned in pairs with the axes of fivefold rotational symmetry of a dodecahedron.

It results from composing the two enantiomorphs

Chirality (mathematics)

In geometry, a figure is chiral if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. For example, a right shoe is different from a left shoe, and clockwise is different from counterclockwise.A chiral object...

 of the compound of six pentagonal prisms

Compound of six pentagonal prisms

This uniform polyhedron compound is a chiral symmetric arrangement of 6 pentagonal prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.- Related polyhedra :...

. 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

Vertex arrangement

In geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes....

 with four uniform polyhedra

Uniform polyhedron

A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive...

 as follows:

Nonconvex great rhombicosidodecahedron	Great dodecicosidodecahedron Great dodecicosidodecahedron In geometry, the great dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U61.- Related polyhedra :It shares its vertex arrangement with the truncated great dodecahedron and the uniform compounds of 6 or 12 pentagonal prisms...	Great rhombidodecahedron Great rhombidodecahedron In geometry, the great rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U73. Its vertex figure is a crossed quadrilateral.- Related polyhedra :...
Truncated great dodecahedron	Compound of six pentagonal prisms Compound of six pentagonal prisms This uniform polyhedron compound is a chiral symmetric arrangement of 6 pentagonal prisms, aligned with the axes of fivefold rotational symmetry of a dodecahedron.- Related polyhedra :...	Compound of twelve pentagonal prisms