A family of easy polyhedra

Let E be a finite set and a family of subsets of E such that the symmetric difference of any two members of this family is at least 2. Let be the complement of in , the set of the subsets of E. In this paper we characterize the convex hull of the characteristic vectors of the elements of . We consider also the polar of these polyhedra and study their links with some well known polyhedra. Note from the Editors  This paper was originally submitted directly to a guest editor appointed for a planned special issue dedicated to the memory of Claude Berge. Unfortunately the issue never materialized and had to be canceled. It was only recently discovered that this paper was never processed.