Assuming that the traffic matrix belongs to a polytope, we describe a new routing paradigm where each traffic matrix is routed a combination of a number of extreme routings. This combination depends on the current traffic matrix. Multipolar routing can be seen as a generalization of both routing and robust static routing. Moreover, the time complexity of multipolar routing is under control since it depends on the number of poles (i.e. the number of extreme routings) which can be defined by the network planner.