Poincaré Formula

The Polyhedral Formula generalized to a surface of Genus $p$.

$$V-E+F=2-2p$$

where $V$ is the number of Vertices, $E$ is the number of Edges, $F$ is the number of faces, and

$$\chi\equiv 2-2p$$

is called the Euler Characteristic.

See also Euler Characteristic, Genus (Surface), Polyhedral Formula

References

Eppstein, D. ``Fourteen Proofs of Euler's Formula: $V-E+F=2$.'' http://www.ics.uci.edu/~eppstein/junkyard/euler/.