(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.

HTML page formatted Mon May 14 11:05:50 2018.

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