Let a closed surface have Genus . Then the Polyhedral Formula becomes the
Poincaré Formula

(1) 
where is the Euler characteristic, sometimes also known as the EulerPoincaré
Characteristic. In terms of the Integral Curvature of the surface ,

(2) 
The Euler characteristic is sometimes also called the Euler Number. It can also be expressed as

(3) 
where is the th Betti Number of the space.
See also Chromatic Number, Map Coloring
© 19969 Eric W. Weisstein
19990525