# The Icosahedron

A polyhedron bounded by twenty equilateral triangles; five meeting at each vertex.

The icosahdedron is one of the five platonic solids.

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

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

Edge ratios:

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

where `e` is the edge length, `r` is the in-radius, `rho` is the inter-radius, and `R` is the circum-radius.