A tiling has finite local complexity (flc) if it contains only finitely many types of patch es with diameter less than some given R0. 'Types of patches' is to be read either as congruence classes of patches, or as translation classes of patches. For instance, the pinwheel tiling is not flc w.r.t. translation classes, but it is flc w.r.t. congruence classes. In our classification, this qualifies the pinwheel tiling to be stored under infinite rotations, and there under finite local complexity.