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”

Related formulas

Variables

rcRadius of the circumscribed sphere (m)
aLength of the edge of the pantagonal face (m)