Let E be a finite set and $${\mathcal{H}}$$ a family of subsets of E such that the symmetric difference of any two members of this family is at least 2. Let $${\mathcal{F}}$$ be the complement of $${\mathcal{H}}$$ in $${\mathcal{P}(E)}$$ , the set of the subsets of E. In this paper we characterize the convex hull of the characteristic vectors of the elements of $${\mathcal{F}}$$ . We consider also the polar of these polyhedra and study their links with some well known polyhedra.