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 (six pairs of parallel pentagons), with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

Images

Transparent model	Spherical tiling
(With animation )	This polyhedron represents a spherical tiling with a density of 3. (One spherical pentagon face is shown above in yellow)
Net	Stellation
× 20 Net for surface geometry; twenty isosceles triangular pyramids, arranged like the faces of an icosahedron	It can also be constructed as the second of three stellations of the dodecahedron, and referenced as Wenninger model [W21].

Related polyhedra

It shares the same edge arrangement as the convex regular icosahedron.

If the great dodecahedron is considered as a properly intersected surface geometry, it has the same topology as a triakis icosahedron with concave pyramids rather than convex ones.

A truncation process applied to the great dodecahedron produces a series of nonconvex uniform polyhedra. Truncating edges down to points produces the dodecadodecahedron as a rectified great dodecahedron. The process completes as a birectification, reducing the original faces down to points, and producing the small stellated dodecahedron.

Name	Small stellated dodecahedron	Dodecadodecahedron	Truncated great dodecahedron	Great dodecahedron
Coxeter-Dynkin diagram
Picture

Usage

• This shape was the basis for the Rubik's Cube-like Alexander's Star puzzle.

See also

• Compound of small stellated dodecahedron and great dodecahedron

External links

• Eric W. Weisstein, Great dodecahedron (Uniform polyhedron) at MathWorld
  • Weisstein, Eric W., "Three dodecahedron stellations", MathWorld.
• Uniform polyhedra and duals
• Metal sculpture of Great Dodecahedron