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”

Related formulas

Variables

rmMidscribed sphere radius (m)
aLength of the pentagonal edge (m)