  For each subcomplex of the standard CW-structure on any torus, we compute the
homology of a certain infinite cyclic regular covering space. In all cases when
the homology is finitely generated, we also compute the cohomology ring. For
aspherical subcomplexes of the torus our computation gives the homology and
cohomology of Bestvina-Brady groups. We compute the cohomological dimension of
each of these groups over any field and over any subring of the rationals.
