A special place of Boolean quadratic polytopes among other combinatorial polytopes

We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set, 3-assignment. For comparing two families of polytopes we use the following method. We say that a family P is affinely reduced to a family Q if for every polytope p ∈ P there exists q ∈ Q such that p is affinely equivalent to q or to a face of q, where dim q = O((dim p)) for some constant k. Under this comparison the above-mentioned families are splitted into two equivalence classes. We show also that these two classes are simpler (in the above sence) than the families of poytopes of the following problems: set covering, traveling salesman, 0-1 knapsack problem, 3-satisfiability, cubic subgraph, partial ordering. In particular, Boolean quadratic polytopes appear as faces of polytopes in every of the mentioned families.