when a planar graph "g" has maximum vertex degree three, its line graph is planar, and every planar embedding of "g" can be extended to an embedding of "l"("g"). however, there exist planar graphs with higher degree whose line graphs are nonplanar. these include, for example, the 5-star "k", the gem graph formed by adding two non-crossing diagonals within a regular pentagon, and all convex polyhedra with a vertex of degree four or more.