  The toric variety corresponding to the Coxeter fan of type A can also be
described as a De Concini-Procesi wonderful model. Using a general result of
Rains which relates cohomology of real De Concini-Procesi models to poset
homology, we give formulas for the Betti numbers of the real toric variety, and
the symmetric group representations on the rational cohomologies. We also show
that the rational cohomology ring is not generated in degree 1.
