Euler polyhedron formula

The Euler polyhedron formula relates the number of faces, edges, and vertices of any polygon or planar graph. The formula is


where \(V\) is the number of vertices, \(E\) is the number of edges, and \(F\) is the number of faces. For example, a cube has 8 vertices, 12 edges, and 6 faces.

Figure 1: The cube.

and \(8-12+6=2\).