  We establish a relation between the two-party Bell inequalities for
two-valued measurements and a high-dimensional convex polytope called the cut
polytope in polyhedral combinatorics. Using this relation, we propose a method,
triangular elimination, to derive tight Bell inequalities from facets of the
cut polytope. This method gives two hundred million inequivalent tight Bell
inequalities from currently known results on the cut polytope. In addition,
this method gives general formulas which represent families of infinitely many
Bell inequalities. These results can be used to examine general properties of
Bell inequalities.
