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Great icosahedron
From Wikipedia, the free encyclopedia
| Great icosahedron | |
|---|---|
 |
|
| Type | Kepler-Poinsot solid |
| Elements | F=20, E=30, V=12 (χ=2) |
| Faces by sides | 20{3} |
| Schläfli symbol | {3,5/2} |
| Wythoff symbol | 5/2 | 2 3 |
| Coxeter-Dynkin |     |
| Symmetry group | Ih |
| References | U53, C69, W41 |
| Properties | Regular nonconvex deltahedron |
 (35)/2 (Vertex figure) |
 Great stellated dodecahedron (dual polyhedron) |
In geometry, the great icosahedron is a Kepler-Poinsot polyhedron. It is one of four nonconvex regular polyhedra. It is composed of 20 triangular faces, with five triangles meeting at each vertex in a pentagrammic sequence.
The 12 vertices match the locations for an icosahedron. The 30 edges are shared by the small stellated dodecahedron.
A transparent model of the great icosahedron (See also Animation)
It is also a stellation of the icosahedron, counted by Wenninger as model [W41] and the 16th of 17 stellations of the icosahedron and 7th of 59 stellations by Coxeter.
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.
