The nonholonomy exhibited by kinematic systems consisting of bodies rolling on top of each other can be used to the purpose of building dexterous mechanism with a minimum hardware complication. Previous work concentrated on manipulation of objects possessing a regular surface. On the other hand, industrial parts are most often irregular, possessing vertices and edges. In this paper we present some results on the description of the set of positions and orientations that polyhedral objects can reach when manipulated by rolling without slipping. An algorithm for planning the manipulation of a polyhedral part from a given configuration to another reachable one, is also presented.