  Traditional representations of graphs and their duals suggest the requirement
that the dual vertices be placed inside their corresponding primal faces, and
the edges of the dual graph cross only their corresponding primal edges. We
consider the problem of simultaneously embedding a planar graph and its dual
into a small integer grid such that the edges are drawn as straight-line
segments and the only crossings are between primal-dual pairs of edges. We
provide a linear-time algorithm that simultaneously embeds a 3-connected planar
graph and its dual on a (2n-2) by (2n-2) integer grid, where n is the total
number of vertices in the graph and its dual. Furthermore our embedding
algorithm satisfies the two natural requirements mentioned above.
