# Regular Icosahedron ( inscribed 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 an inscribed sphere (tangent to each of the icosahedron’s faces) is related to the edge length of the triangle face and the “golden ratio”.

Related formulas## Variables

r_{i} | Inscribed sphere radius (m) |

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