Euler theorem

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For every polyhedron the number $V$ of its vertices plus the number $F$ of its faces minus the number $E$ of its edges is equal to 2:


Euler's theorem hold for polyhedrons of genus $0$; for polyhedrons of genus $p$ the relation


holds. This theorem was proved by L. Euler (1758); the relation \eqref{*} was known to R. Descartes (1620).

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Euler theorem. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article