  Aigner and Fromme initiated the systematic study of the cop number of a graph
by proving the elegant and sharp result that in every connected planar graph,
three cops are sufficient to win a natural pursuit game against a single
robber. This game, introduced by Nowakowski and Winkler, is commonly known as
Cops and Robbers in the combinatorial literature. We extend this study to
directed planar graphs, and establish separation from the undirected setting.
We exhibit a geometric construction which shows that a more sophisticated
robber strategy can indefinitely evade three cops on a particular strongly
connected planar directed graph.
