# Regular Dodecahedron ( midscribed 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

A midscribed sphere is the sphere which touches the middle of each edge of the pentagonal faces. The midradius is related to the edge of the face and the “golden ratio”

## Variables

r_{m} | Midscribed sphere radius (m) |

a | Length of the pentagonal edge (m) |