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Small stellated dodecahedron
From Wikipedia, the free encyclopedia
| Small stellated dodecahedron | |
|---|---|
 |
|
| Type | Kepler-Poinsot solid |
| Elements | F=12, E=30, V=12 (χ=-6) |
| Faces by sides | 12{5/2} |
| Schläfli symbol | {5/2,5} |
| Wythoff symbol | 5 | 25/2 |
| Coxeter-Dynkin |     |
| Symmetry group | Ih |
| References | U34, C43, W20 |
| Properties | Regular nonconvex |
 (5/2)5 (Vertex figure) |
 Great dodecahedron (dual polyhedron) |
In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each vertex.
The 12 vertices match the locations for an icosahedron. The 30 edges are shared by the great icosahedron.
It is considered the first of three stellations of the dodecahedron.
If the pentagrammic faces are considered as 5 triangular faces, it shares the same surface topology as the pentakis dodecahedron, but with much taller isosceles triangle faces.
A transparent model of the small stellated dodecahedron (See also Animated)
It can also be constructed as the first of four stellations of the dodecahedron, and referenced as Wenninger model [W20].
The stellation facets for construction are:
- Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-521-09859-9.
- Coxeter, H. S. M. (1938). The Fifty-Nine Icosahedra. Springer-Verlag, New York, Berlin, Heidelberg. ISBN 0-387-90770-X.
