A formula due to Euler (in fact, a special case of the Euler characteristic in R3). Take any 3 dimensional polytope (i.e. a solid with planar faces) with no holes in it. Count its 0-, 1-, and 2-dimensional features: Then V-E+F=2. Always.

For instance, consider a regular dodecahedron. It has 12 faces (F=12), each a pentagon, for a total of 30 edges (recall that each edge is shared by 2 faces, so E=30). 3 faces meet at each vertex, so there are 20 vertices (V=20). Amazingly, 12-30+20=2, as promised.

See also Euler formula.