an alternative construction, the medial graph, coincides with the line graph for planar graphs with maximum degree three, but is always planar. it has the same vertices as the line graph, but potentially fewer edges: two vertices of the medial graph are adjacent if and only if the corresponding two edges are consecutive on some face of the planar embedding. the medial graph of the dual graph of a plane graph is the same as the medial graph of the original plane graph.