# The Small Stellated Dodecahedron

A non-convex polyhedron bounded by twelve intersecting pentagrams; five meeting at each vertex.

The small stellated dodecahecahedron is one of the four Kepler-Poinsot Star Polyhedra, and is also the first stellation of the dodecahedron.

Vertex Symbol |
Wythoff Symbol |
No. of Vertices |
No. of Edges |
No. of Faces |
Symmetry Group |
Dual Polyhedron |

(5/2)^{5} |
5 | 2 5/2 | 12 | 30 | 12 | A_{5}×C_{2} |
Great Dodecahedron |

Edge ratios:

- `e/r = sqrt(10+2sqrt(5))`
- `e/rho = 1 + sqrt(5)`
- `e/R = sqrt( (10+2sqrt(5))/(5) )`
- `e/e_(12) = (3+sqrt(5))/2`

where `e` is the edge length, `r` is the in-radius, `rho` is the inter-radius, `R` is the circum-radius, and `e_(12)` is the edge of the inner dodecahedron.