Two 0-1 integer programs that are equivalent, in that they have the same objective function and the same set of feasible solutions, may have quite different linear programming relaxations: a linear programming relaxation can be viewed geometrically, as a convex polytope that includes all feasible solutions and excludes all other 0-1 vectors, and infinitely many different polytopes have this property. Ideally, one would like to use as a relaxation the convex hull of the feasible solutions; linear programming on this polytope would automatically yield the correct solution to the original integer program. However, in general, this polytope will have exponentially many facets and be difficult to construct. Typical relaxations, such as the relaxation of the set cover problem discussed earlier, form a polytope that strictly contains the convex hull and has vertices other than the 0-1 vectors that solve the unrelaxed problem.