A Local Characterization of Combinatorial Multihedrality in Tilings

Details A Local Characterization of Combinatorial Multihedrality in Tilings A Local Characterization of Combinatorial Multihedrality in Tilings

2008-09-12

arxiv.org/abs/0809.2291v1

Mathematics

Metric Geometry

10 pages (to appear in Contributions to Discrete Mathematics)

Scientific paper

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 an earlier paper, which characterizes the case of combinatorial tile-transitivity.

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