  A basic assumption of tiling theory is that adjacent tiles can meet in only a
finite number of ways, up to rigid motions. However, there are many interesting
tiling spaces that do not have this property. They have "fault lines", along
which tiles can slide past one another. We investigate the topology of a
certain class of tiling spaces of this type. We show that they can be written
as inverse limits of CW complexes, and their Cech cohomology is related to
properties of the fault lines.
