# The Great Icosahedron

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

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

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

3^{5/2} |
5/2 | 2 3 | 12 | 30 | 20 | A_{5}×C_{2} |
Great Stellated Dodecahedron |

Edge ratios:

- `e/r = sqrt(10+2sqrt(5))`
- `e/rho = 1 + sqrt(5)`
- `e/R = sqrt( (10+2sqrt(5))/5 )`
- `e/e_(20) = (7+3sqrt(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_(20)` is the edge of the inner icosahedron.