Small stellated dodecahedron
In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {5⁄2,5}. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeting at each vertex.
| Small stellated dodecahedron | |
|---|---|
| Type | Kepler–Poinsot polyhedron |
| Stellation core | regular dodecahedron |
| Elements | F = 12, E = 30 V = 12 (χ = -6) |
| Faces by sides | 12 5 |
| Schläfli symbol | {5⁄2,5} |
| Face configuration | V(55)/2 |
| Wythoff symbol | 5 | 2 5⁄2 |
| Coxeter diagram | |
| Symmetry group | Ih, H3, [5,3], (*532) |
| References | U34, C43, W20 |
| Properties | Regular nonconvex |
(5⁄2)5 (Vertex figure) |
Great dodecahedron (dual polyhedron) |
It shares the same vertex arrangement as the convex regular icosahedron. It also shares the same edge arrangement with the great icosahedron, with which it forms a degenerate uniform compound figure.
It is the second of four stellations of the dodecahedron (including the original dodecahedron itself).
The small stellated dodecahedron can be constructed analogously to the pentagram, its two-dimensional analogue, via the extension of the edges (1-faces) of the core polytope until a point is reached where they intersect.