Part of the Graduate Texts in Mathematics book series (GTM, volume 47)
The Euler characteristic
Let K be a finite complex, of dimension ⩽ 2. The Euler characteristic of K is the alternating sum
where V, E, and F are respectively the number of vertices, edges, and 2-faces of K.
$$x\left( K \right) = V - E + F,$$
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© Springer Science+Business Media New York 1977