Regular Icosahedron ( circumscribed sphere radius)

Description

An icosahedron is a polyhedron with 20 triangular faces, 30 edges and 12 vertices. A regular icosahedron has 20 identical equilateral faces, with five of the triangular faces meeting at each vertex. If the edge length of a regular icosahedron is “a”, the radius of a circumscribed sphere (one that touches the icosahedron at all vertices) is related with the length of the edge of the triangle face and the “golden ratio”

Related formulas

Variables

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