# Regular Dodecahedron ( circumscribed sphere radius

## Description

A regular dodecahedron is a polyhedron composed of 12 regular pentagonal faces, with three meeting at each vertex. It has 20 vertices, 30 edges and 160 diagonals.

If the edge length of a regular dodecahedron is “a”, the radius of a circumscribed sphere (one that touches the dodecahedron at all vertices) is related with this edge and the “golden ratio”

## Variables

r_{c} | Radius of the circumscribed sphere (m) |

a | Length of the edge of the pantagonal face (m) |