A

David

Darling

Euler's formula for polyhedra

Euler's formula for polyhedra is the earliest known equation in topology. If F is the number of faces of a polyhedron, E the number of edges, and V the number of vertices, Euler's formula can be written as

 

F - E + V = 2.

 

For example, the surface of a cube has six (square) faces, twelve edges, and eight vertices and, sure enough, 6 - 12 + 8 = 2. The quantity F - E + V is known as the Euler characteristic.