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)
Here F, E, V, L, B and G are respectively the number of faces, edges, vertices, face's inner loop, bodies, and genus (handles or through holes). If the solid is a simple one, the Euler Eq. holds good.
F - E + V = 2