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{{ printedBook.courseTrack.name }} {{ printedBook.name }} The sum of the number of faces $(F)$ and vertices $(V)$ of a polyhedron is two more than the number of its edges $(E)$.

$F+V=E+2$

As an example, this can be verified for the following polyhedron.

The above polyhedron has $7$ faces, $10$ vertices, and $15$ edges.

$F+V7+1017 =?E+2=?15+2=17✓ $

Euler's formula takes a slightly different form in two dimensions.

$F+V=E+1$

Here, $F$ is the number of regions formed by $V$ vertices, linked by $E$ segments. This formula can be verified for the net of the previous polyhedron.

The net shown has $7$ regions, $18$ vertices, and $24$ segments.

$F+V7+1825 =?E+1=?24+1=25✓ $