| Great dodecahedron | |
|---|---|
 |
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| Type | Kepler-Poinsot solid |
| Stellation core | dodecahedron |
| 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 |
| Coxeter-Dynkin |     |
| Symmetry group | Ih |
| References | U35, C44, W21 |
| Properties | Regular nonconvex |
 (55)/2 (Vertex figure) |
 Small stellated dodecahedron (dual polyhedron) |
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 parallel pentagons), with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.
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 (Animation)
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:
