Regular Icosahedron ( midscribed sphere radius)


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 midscribed sphere ( which touches the middle of each edge, ) is related with the length of the edge of the triangle face and the “golden ratio”

Related formulas


rmRadius of the midscribed sphere (m)
aLength of the edge of the triangle face (m)