Compound of five small stellated dodecahedra

Last updated
Compound of five small stellated dodecahedra
UC51-5 small stellated dodecahedra.png
Type Uniform compound
IndexUC51
Polyhedra5 small stellated dodecahedra
Faces60 pentagrams
Edges150
Vertices60
Symmetry group icosahedral (Ih)
Subgroup restricting to one constituent pyritohedral (Th)

This uniform polyhedron compound is a composition of 5 small stellated dodecahedra, in the same arrangement as in the compound of 5 icosahedra.

It is one of only five polyhedral compounds (along with the compound of six tetrahedra, the compound of two great dodecahedra, the compound of five great dodecahedra, and the compound of two small stellated dodecahedra) which is vertex-transitive and face-transitive but not edge-transitive.

Related Research Articles

In geometry, a dodecahedron or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120.

Kepler–Poinsot polyhedron

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.

A polyhedral compound is a figure that is composed of several polyhedra sharing a common centre. They are the three-dimensional analogs of polygonal compounds such as the hexagram.

Rhombicosidodecahedron Archimedean solid

In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent definitions are used; a common one is that the faces are congruent regular polygons which are assembled in the same way around each vertex.

Great dodecahedron

In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol {5,5/2} and Coxeter–Dynkin diagram of . It is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces, intersecting each other making a pentagrammic path, with five pentagons meeting at each vertex.

Small stellated dodecahedron A Kepler-Poinsot polyhedron

In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {52,5}. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each vertex.

Great icosahedron

In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra, with Schläfli symbol {3,52} and Coxeter-Dynkin diagram of . It is composed of 20 intersecting triangular faces, having five triangles meeting at each vertex in a pentagrammic sequence.

Honeycomb (geometry) Tiling of 3-or-more dimensional euclidian or hyperbolic space

In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions. Its dimension can be clarified as n-honeycomb for a honeycomb of n-dimensional space.

Compound of five cubes Polyhedral compound

The compound of five cubes is one of the five regular polyhedral compounds. It was first described by Edmund Hess in 1876.

Compound of two tetrahedra Polyhedral compound

In geometry, a compound of two tetrahedra is constructed by two overlapping tetrahedra, usually implied as regular tetrahedra.

Compound of two great dodecahedra Polyhedral compound

This uniform polyhedron compound is a composition of 2 great dodecahedra, in the same arrangement as in the compound of 2 icosahedra.

Compound of two small stellated dodecahedra Polyhedral compound

This uniform polyhedron compound is a composition of 2 small stellated dodecahedra, in the same arrangement as in the compound of 2 icosahedra.

Compound of five great dodecahedra Polyhedral compound

This uniform polyhedron compound is a composition of 5 great dodecahedra, in the same arrangement as in the compound of 5 icosahedra.

Compound of six tetrahedra Polyhedral compound

The compound of six tetrahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 6 tetrahedra. It can be constructed by inscribing a stella octangula within each cube in the compound of three cubes, or by stellating each octahedron in the compound of three octahedra.

Decagram (geometry) 10-pointed star polygon

In geometry, a decagram is a 10-point star polygon. There is one regular decagram, containing the vertices of a regular decagon, but connected by every third point. Its Schläfli symbol is {10/3}.

Small complex rhombicosidodecahedron

In geometry, the small complex rhombicosidodecahedron is a degenerate uniform star polyhedron. It has 62 faces, 120 (doubled) edges and 20 vertices. All edges are doubled, sharing 4 faces, but are considered as two overlapping edges as a topological polyhedron.

Stellated rhombic dodecahedral honeycomb

The stellated rhombic dodecahedral honeycomb is a space-filling tessellation in Euclidean 3-space made up of copies of stellated rhombic dodecahedron cells. Six stellated rhombic dodecahedra meet at each vertex. This honeycomb is cell-transitive, edge-transitive and vertex-transitive.

References