# 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

r_{c} | Radius of the circumscribed sphere (m) |

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