  We derive a homeomorphism invariant for those tiling spaces which are made by
rather general substitution rules on polygonal tiles, including those tilings,
like the pinwheel, which contain tiles in infinitely many orientations. The
invariant is a quotient of Cech cohomology, is easily computed directly from
the substitution rule, and distinguishes many examples, including most
pinwheel-like tiling spaces. We also introduce a module structure on cohomology
which is very convenient as well as of intuitive value.
