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Euler's formula for polyhedra





The earliest known equation in topology. If F is the number of faces of a polygon, 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.


Related category

   • SOLIDS AND SURFACES