Compound of twenty triangular 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	UC33
Polyhedra	20 triangular prism Triangular prism In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.... s
Faces	40 triangle Triangle A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted .... s, 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	3-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:...  (D3)

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 20 triangular prism

Triangular prism

In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides....

s, aligned in pairs with the axes of three-fold rotational symmetry of an icosahedron

Icosahedron

In geometry, an icosahedron is a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. It is one of the five Platonic solids....

.

It results from composing the two enantiomorphs of the compound of 10 triangular prisms

Compound of ten triangular prisms

This uniform polyhedron compound is a chiral symmetric arrangement of 10 triangular prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron.- Relatde polyhedra :...

. In doing so, the vertices of the two enantiomorphs coincide, with the result that the full compound has two triangular 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 three uniform polyhedra

Uniform polyhedron

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

 as follows:

convex hull Convex hull In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the minimal convex set containing X....	Rhombidodecadodecahedron	Icosidodecadodecahedron Icosidodecadodecahedron In geometry, the icosidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U44. Its vertex figure is a crossed quadrilateral.- Related polyhedra :It shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms...
Rhombicosahedron Rhombicosahedron In geometry, the rhombicosahedron is a nonconvex uniform polyhedron, indexed as U56. Its vertex figure is an antiparallelogram.- Related polyhedra :...	Compound of ten triangular prisms Compound of ten triangular prisms This uniform polyhedron compound is a chiral symmetric arrangement of 10 triangular prisms, aligned with the axes of three-fold rotational symmetry of an icosahedron.- Relatde polyhedra :...	Compound of twenty triangular prisms