The empirical study of impossible figures requires that independent variables be well-specified. This paper provides an aid for such a task by developing a classification system which partitions cornered torus figures into meaningful subsets. These can be used to identify both formal and psychological properties of known as well as unknown possible and impossible figures in much the same manner as with the periodic table of chemical elements. The classification is polytopic (four dimensional) and is formally, not empirically, derived. Coherent three-dimensional and two-dimensional forms of the system are possible without loss of information.
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