Category:Definitions/Euler Characteristic of Surface

This category contains definitions related to Euler Characteristic of Surface.
Related results can be found in Category:Euler Characteristic of Surface.

Let $S$ be a surface.

Let $T$ be a triangulation of $S$.

The Euler characteristic of $S$ is written $\map \chi S$ and is defined as:

$\map \chi S = v - e + f$

where:

$v = \size V$ is the number of vertices of $T$

$e = \size E$ is the number of edges of $T$

$f$ is the number of faces of $T$.