Compound of five small cubicuboctahedra
Encyclopedia
| Compound of five small cubicuboctahedra | |
|---|---|
 |
|
| 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 | UC64 |
| Polyhedra | 5 small cubicuboctahedra Small cubicuboctahedron In geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13. It has 20 faces , 48 edges, and 24 vertices. Its vertex figure is a crossed quadrilateral.- Related polyhedra :... |
| Faces | 40 triangles, 30 squares Square (geometry) In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles... , 30 octagons |
| 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 small cubicuboctahedra
Small cubicuboctahedron
In geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13. It has 20 faces , 48 edges, and 24 vertices. Its vertex figure is a crossed quadrilateral.- Related polyhedra :...
, in the same 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....
as the compound of 5 small rhombicuboctahedra
Compound of five small rhombicuboctahedra
This uniform polyhedron compound is a composition of 5 small rhombicuboctahedra, in the same vertex arrangement the compound of 5 stellated truncated cubes....
.