# The Great Dodecahedron

A non-convex polyhedron bounded by twelve intersecting pentagonal faces. It has twelve '5/2' star vertices.

The great dodecahedron is one of the four Kepler-Poinsot Star Polyhedra, and is also the second stellation of the dodecahedron.

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

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

Edge ratios:

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