Great stellated dodecahedron
From Wikipedia, the free encyclopedia
| Great stellated dodecahedron | |
|---|---|
 |
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| Type | Kepler-Poinsot solid |
| Stellation core | dodecahedron |
| Elements | F = 12, E = 30 V = 20 (χ = 2) |
| Faces by sides | 12{5/2} |
| Schläfli symbol | {5/2,3} |
| Wythoff symbol | 3 | 25/2 |
| Coxeter-Dynkin |     |
| Symmetry group | Ih |
| References | U52, C68, W22 |
| Properties | Regular nonconvex |
 (5/2)3 (Vertex figure) |
 Great icosahedron (dual polyhedron) |
In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron. It is one of four nonconvex regular polyhedra.
It is composed of 12 pentagrammic faces, with three pentagrams meeting at each vertex.
It shares its vertex arrangement with the regualar dodecahedron.
Shaving the triangular pyramids off results in an icosahedron.
If the pentagrammic faces are broken into triangles, it is topologically related to the triakis icosahedron, with the same face connectivity, but much taller isosceles triangle faces.
Transparent great stellated dodecahedron (Animation)
[edit] As a stellation
It can also be constructed as the third of three stellations of the dodecahedron, and referenced as Wenninger model [W22].
The stellation facets for construction are:
[edit] References
- Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-521-09859-9.
