Euler formula for a sphere
= Euler formula for a sphere
{c}
{title2=$V-E+F=2$}
For a finite cell decomposition of the <sphere> into polygonal faces, the numbers of vertices, edges and faces satisfy the displayed formula. Triangulating faces preserves $V-E+F$ because each added diagonal adds one edge and one face. This is the spherical form of <Euler formula for a connected planar graph>, where the plane's exterior face is included.