# The Truncated Icosahedron

A semi-regular polyhedron with two hexagons and a pentagon meeting at each vertex.

The truncated icosahedron is one of the thirteen archimedian solids. It can be created by slicing suitable sections off the vertices of either a dodecahedron or an icosahedron and thus may be inscribed in either solid.

Vertex Symbol |
Wythoff Symbol |
No. of Vertices |
No. of Edges |
{5} Faces |
{6} Faces |
Symmetry Group |
Dual Polyhedron |

5.6.6 | 2 5 | 3 | 60 | 90 | 12 | 20 | A_{5}×C_{2} |
Pentakis Dodecahedron |

Edge ratios:

- `e/rho = (sqrt(5)-1)/3`
- `e/R = sqrt((58-18sqrt(5))/109)`
- `e/(e_12) = (7+5sqrt(5))/38`
- `e/(e_20) = 1/3`

where `e` is the edge length, `rho` is the inter-radius, `R` is the circum-radius, `e_12` is the edge of the circumscribing dodecahedron, and `e_20` is the edge of the circumscribing icosahedron.