  Stanley (1986) introduced the order polytope and chain polytope of a
partially ordered set and showed that they are related by a piecewise-linear
homeomorphism. In this paper we view order and chain polytopes as instances of
distributive and anti-blocking polytopes, respectively. Both these classes of
polytopes are defined in terms of the componentwise partial order on $\mathbb
R^n$. We generalize Stanley's PL-homeomorphism to a large class of distributive
polyhedra using infinite walks in marked networks.
