How to count the number of faces or regions of a graph How to count the number of faces or regions of a graph such as the below graph:


The graph has 12 vertices and 17 edges. But I am unable to find the number of faces of the graph. I don't know how to find the faces. Help me to find the number of faces.
The depicted graph has a $K_{3,3}$ (complete bipartite graph on six vertices) as a minor. By Kuratowski's theorem such graph is not a planar graph, hence it makes no sense to talk about its faces, unless you embed such graph in a torus or in a surface with genus $\geq 1$:
Euler's theorem $f+n-m=2$.
$n$: number of vertices.
$m$: number of edges.
$f$: number of faces.