Widely used methods for identifying crystal structure in atomistic simulations are limited in practice to a handful of simple structures, leaving many important crystalline systems without automated classification techniques. Voronoi topology analysis offers a route to classifying arbitrary crystalline and defect environments, but realizing this potential first requires enumerating the Voronoi cell topologies that can arise under thermal perturbation of a structure of interest. We present an algorithm that deterministically enumerates all Voronoi cell topologies arising from generic infinitesimal perturbations of an arbitrary crystal structure, producing structural classifiers that extend automated identification to general crystalline systems. We demonstrate the approach on several structures of general interest.

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