A regular icosahedron is one of the five Platonic solids.
It has 20 faces, 30 edges and (how many?
Derive the formulas for its area and volume.
Euler's law: F + V = E + 2 for any non-self intersecting polyhedron.
For the icosahedron, 20 + V = 30 + 2
So, number of vertices, V = 12
(the easy part.)