Complex sentence: The same fact can be expressed in the theory of matroids: if "M" is the graphic matroid of a graph "G", then the dual matroid of "M" is a graphic matroid if and only if "G" is planar.
Split into simpler sentences: The same fact can be expressed in the theory of matroids. Then Whitney's planarity criterion can be rephrased as stating that the dual matroid of a graphic matroid is itself a graphic matroid if and only if the underlying graph of is planar.