User:Joost P. Vermeer

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


 * $$r_u = \frac{a}{4} \sqrt{10 +2\sqrt{5}}$$

Spere enclosed volume is


 * $$V = \frac{4}{3}\pi r^3$$