(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

Go to the Dictionary of Algorithms and Data Structures home page.

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