On the formal definition of mesh or region for a planar graph

A graphical representation of a planar graph divides the plane into the regions or mesh (as they are called in some applications, for example in circuit theory).

Yes, the above is intuitive, but what I did not find in the classic textbooks on graph theory is a formal definition of the mesh related to the definition of the graph as a pair of sets of vertices and edges. In particular, is there a formal definition of the mesh (or region) of a graph that does not rely on its graphical representation or that relies on a formalization of it?