Compound of five great rhombihexahedra
Encyclopedia
Compound of five great rhombihexahedra
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 UC66
Polyhedra 5 great rhombihexahedra
Great rhombihexahedron
In geometry, the great rhombihexahedron is a nonconvex uniform polyhedron, indexed as U21. Its dual is the great rhombihexacron. Its vertex figure is a crossed quadrilateral.- Related polyhedra :...

Faces 60 squares
Square (geometry)
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...

, 30 octagram
Octagram
In geometry, an octagram is an eight-sided star polygon.- Geometry :In general, an octagram is any self-intersecting octagon ....

s
Edges 240
Vertices 120
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
pyritohedral
Tetrahedral symmetry
150px|right|thumb|A regular [[tetrahedron]], an example of a solid with full tetrahedral symmetryA regular tetrahedron has 12 rotational symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.The group of all symmetries is isomorphic to the group...

 (Th)

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 composition of 5 great rhombihexahedra
Great rhombihexahedron
In geometry, the great rhombihexahedron is a nonconvex uniform polyhedron, indexed as U21. Its dual is the great rhombihexacron. Its vertex figure is a crossed quadrilateral.- Related polyhedra :...

, in the same arrangement as the compound of 5 uniform great rhombicuboctahedra
Compound of five uniform great rhombicuboctahedra
This uniform polyhedron compound is a composition of 5 uniform great rhombicuboctahedra, in the same arrangement the compound of 5 truncated cubes....

.
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