# Dodecahedron regular (inscribed 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.

The radius of an inscribed sphere (tangent to each of the dodecahedron faces) is related to the edge of the pentagonal face and the “golden ratio”

## Variables

r_{i} | Inscribed spheer radius (m) |

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