The study shows a local characterization of combinatorial multihedral tilings using centered coronas, highlighting its link to combinatorial automorphism groups.
A locally finite face-to-face tiling of euclidean d-space by convex polytopes is called { combinatorially multihedral\/} if its combinatorial automorphism group has only finitely many orbits on the tiles. The paper describes a local characterization of combinatorially multihedral tilings in terms of centered coronas. This generalizes the Local Theorem for Monotypic Tilings, established in {dolsch}, which characterizes the case of combinatorial tile-transitivity.
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Долбилин et al. (2009) studied this question.
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