Matthew Hastings Microsoft Station Q I'll explain how a version of Kirby's torus trick from topology can be used in many cases to reduce the problem of classifying aperiodic quantum systems to the simpler problem of classifying periodic quantum systems. For free fermions, this provides an alternative to the idea of textures introduced by Kitaev. I'll then discuss the application of this trick to other phases which are topologically nontrivial but lack anyons.