Polyhedra and Euler's Formula
The b-rep of a polyhedra that are holomorphic to a sphere are topologically valid if they satisfy the following equations :
F - E + V - L = 2 (B - G)
where F, E, V, L, B and G are the number of faces, edges, vertices, face's inner loop, bodies, and genus (handles or through holes) respectively. If the solid is a simple one, the Euler holds good.
F - E + V = 2