# Euler Characteristic > [!Example] Euler Characteristic > The **Euler characteristic** is a topological invariant originally defined for the *surfaces of polyhedra* as > $\chi=V-E+F$ > where $V$, $E$, and $F$ are the number of *vertices*, *edges*, and *faces*, respectively, of a polyhedron. ## Euler's polyhedron formula > [!Example] Euler's polyhedron formula > **Euler's polyhedron formula** refers to the equation > $\chi=V-E+F=2$ > which is true for all *convex* polyhedra. This formula is also true for [[Connected Graph|connected]] [[Planar Graph|planar graphs]] and thus the [[Schlegel diagram]] of all convex polyhedra are also connected planar graphs. ![[EulerCharacteristicCube.svg|600]]