  We establish that the extension complexity of the nXn correlation polytope is
at least 1.5^n by a short proof that is self-contained except for using the
fact that every face of a polyhedron is the intersection of all facets it is
contained in. The main innovative aspect of the proof is a simple combinatorial
argument showing that the rectangle covering number of the unique-disjointness
matrix is at least 1.5^n, and thus the nondeterministic communication
complexity of the unique-disjointness predicate is at least .58n. We thereby
slightly improve on the previously best known lower bounds 1.24^n and .31n,
respectively.
