# The Truncated Dodecahedron

A semi-regular polyhedron with two decagons and a triangle meeting at each vetex.

The truncated dodecahedron 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 |
{3} Faces |
{10} Faces |
Symmetry Group |
Dual Polyhedron |

3.10.10 | 2 3 | 5 | 60 | 90 | 20 | 12 | A_{5}×C_{2} |
Triakis Icosahedron |

Edge ratios:

- `e/rho = (3sqrt(5)-5)/5`
- `e/R = sqrt((74-30sqrt(5))/61)`
- `e/(e_12) = sqrt(5)/5`
- `e/(e_20) = (3sqrt(5)-1)/22`

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.