Small stellated dodecahedron
From Wikipedia, the free encyclopedia
| Small stellated 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{5/2} |
| 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.
It shares the same vertex arrangement as the convex regular icosahedron. It also shares the same edge arrangement as 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)
Contents |
[edit] As a stellation
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:
[edit] Paper construction
Small stellated dodecahedra can be constructed out of paper or cardstock by connecting together 12 five-sided isosceles pyramids in the same manner as the pentagons in a regular dodecahedron. With an opaque material, this visually represents the exterior portion of each pentagrammic face.
A net for creating a small stellated dodecahedron might look something like this:
[edit] In art
- A small stellated dodecahedron is seen featured in Gravitation by M. C. Escher.
- It can also be seen in a mosaic by Paolo Uccello circa 1430.
[edit] References
- 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.
