Icosahedron - Area and Volume

Area and Volume

The surface area A and the volume V of a regular icosahedron of edge length a are:

 A010527
 A102208

The latter is F=20 times the volume of a general tetrahedron with apex at the center of the inscribed sphere, where the volume of the tetrahedron is one third times the base area √3a2/4 times its height ri.

The volume filling factor of the circumscribed sphere is

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