Definition: For convex polyhedron, V - E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces.
Note: Ernst Steinitz gave two inequalities that, if met, guarantee the existence of a polyhedron for three positive integers satisfying Euler's formula.
(As of 2012) no one has found an equivalent formula for four-dimensional polyhedrons.
If you have suggestions, corrections, or comments, please get in touch with Paul Black.
Entry modified 14 May 2018.
HTML page formatted Wed Mar 13 12:42:45 2019.
Cite this as:
Paul E. Black, "Euler's formula", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 14 May 2018. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/EulersFormula.html