Most of the previous ideas generalize nicely for the case of a polyhedral robot that is capable of translation only in a 3D world that contains polyhedral obstacles. If and are convex polyhedra, the resulting is a convex polyhedron.

There are three different kinds of contacts that each lead to half-spaces in :

**Type FV:**A face of and a vertex of**Type VF:**A vertex of and a face of**Type EE:**An edge of and an edge of .

Steven M LaValle 2012-04-20