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Euler theorem

From Encyclopedia of Mathematics
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For every polyhedron the number of its vertices plus the number of its faces minus the number of its edges is equal to 2:

(*)

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

holds. This theorem was proved by L. Euler (1758); the relation (*) 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=31997
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article