dual graph

A second graph built from a planar drawing's faces -- one vertex per face, one edge per crossing of an original edge -- that swaps the roles of vertices and faces.

Given a plane embedding of $G$ , its dual $G^*$ has one vertex per face of $G$ and one edge per edge of $G$ , joining the two faces that edge borders. A graph has a geometric dual iff it is planar (theorem: whitneys-duality-theorem).