Definition:Planar Graph

Planar
A planar graph is a graph which can be drawn in the plane (e.g. on a piece of paper) without any of the edges crossing over, that is, meeting at points other than the vertices.

This is a planar graph:



Face
The faces of a planar graph are the areas which are surrounded by edges.

In the above, the faces are $$ABHC, CEGH, ACD, CDFE, ADFEGHIHB$$.

Non-Planar
A non-planar graph is a graph which is not planar.

This is a non-planar graph: