NIST

Euler's formula

(definition)

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.

Author: PEB


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Entry modified 14 May 2018.
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Cite this as:
Paul E. Black, "Euler's formula", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 14 May 2018. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/EulersFormula.html