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A local characterization of combinatorial multihedrality in tilings

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A locally finite face-to-face tiling of euclidean $d$-space by convex polytopes is called {em 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 cite{dolsch}, which characterizes the case of combinatorial tile-transitivity.


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