  In this article, we study the cohomology ring of real moment-angle complexes
over a simplicial complex $K$. Combinatorial generators for the cohomology can
be given in terms of $K$. For $K$ the boundary of an $n$-gon, we give a full
description of the multiplicative structure of the cohomology ring in terms of
the combinatorial generators. As a consequence, it is evident that these
generators do not form a symplectic basis, unlike the case for moment-angle
complexes.
