Euler theorem
From Encyclopedia of Mathematics
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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:
$$V+F-E=2.\label{*}\tag{*}$$
Euler's theorem hold for polyhedrons of genus $0$; for polyhedrons of genus $p$ the relation
$$V+F-E=2-2p$$
holds. This theorem was proved by L. Euler (1758); the relation \eqref{*} was known to R. Descartes (1620).
How to Cite This Entry:
Euler theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euler_theorem&oldid=44767
Euler theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euler_theorem&oldid=44767
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article