  Quasiperiodic patterns described by polyhedral "atomic surfaces" and
admitting matching rules are considered. It is shown that the cohomology ring
of the continuous hull of such patterns is isomorphic to that of the complement
of a torus $T^N$ to an arrangement $A$ of thickened affine tori of codimension
two. Explicit computation of Betti numbers for several two-dimensional tilings
and for the icosahedral Ammann-Kramer tiling confirms in most cases the results
obtained previously by different methods. The cohomology groups of $T^N
\backslash A$ have a natural structure of a right module over the group ring of
the space symmetry group of the pattern and can be decomposed in a direct sum
of its irreducible representations. An example of such decomposition is shown
for the Ammann-Kramer tiling.
