Edge-disjoint maximal planar graphs

We show that if n ⩾ 6m then it is possible to construct m edge-disjoint maximal planar graphs on a set of n vertices, but that it is not possible if n < 6m − 1. We also show that given a pair of edge-disjoint maximal planar graphs, and a specified face in one, there exist at least three faces in the other which are vertex-disjoint from the specified face. For three edge-disjoint maximal planar graphs there exist three faces, one from each graph, which are vertex-disjoint.