GREAT DODECAHEDRON

In geometry, the 'great dodecahedron' is a Kepler-Poinsot polyhedron. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces (six pairs of parrallel pentagons), with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

Contents

Features

As a stellation

External links

Features

The convex edges (where the pentagon edges meet) share the same edge arrangement as the convex regular icosahedron.
The concave edges (where the pentagon surfaces intersect) share the same edge arrangement as the small stellated dodecahedron.
This shape was the basis for the Rubik's Cube-like Alexander's Star puzzle.
It is considered the second of three stellations of the dodecahedron.
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.

Transparent great dodecahedron ()

As a stellation

It can also be constructed as the second of four stellations of the dodecahedron, and referenced as Wenninger model [W21].
The stellation facets for construction are:
:

External links

★ MathWorld: Great Dodecahedron

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★ MathWorld: 3 stellations of the dodecahedron

★ Metal sculpture of Great Dodecahedron