Great dodecahedron
From Wikipedia, the free encyclopedia
| Great dodecahedron | |
|---|---|
 (Click here for rotating model) |
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| Type | Kepler-Poinsot solid |
| Elements | F=12, E=30, V=12 (χ=-6) |
| Faces by sides | 12{5} |
| Schläfli symbol | {5,5/2} |
| Wythoff symbol | 5/2 | 2 5 |
| Symmetry group | Ih |
| Index references | U35, C44, W21 |
| Dual | Small stellated dodecahedron |
| Properties | Regular nonconvex |
 Vertex figure (5.5.5.5.5)/2 |
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In geometry, the great dodecahedron is a Kepler-Poinsot solid. It is one of four nonconvex regular polyhedra.
It is composed of 12 pentagonal faces, with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.
The 12 vertices match the locations for an icosahedron.
This shape was the basis for the Rubik's Cube-like Alexander's Star puzzle.
Shaving off the concave part results in a dodecahedron.
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 (Animation)
[edit] 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:
