Dirk Frettlöh ; Alexey Garber - Symmetries of Monocoronal Tilings

dmtcs:2142 - Discrete Mathematics & Theoretical Computer Science, October 5, 2015, Vol. 17 no.2 - https://doi.org/10.46298/dmtcs.2142
Symmetries of Monocoronal TilingsArticle

Authors: Dirk Frettlöh 1; Alexey Garber ORCID2

  • 1 Technische Fakultät, Universität Bielefeld
  • 2 Department of Mathematics, The University of Texas at Brownsville

The vertex corona of a vertex of some tiling is the vertex together with the adjacent tiles. A tiling where all vertex coronae are congruent is called monocoronal. We provide a classification of monocoronal tilings in the Euclidean plane and derive a list of all possible symmetry groups of monocoronal tilings. In particular, any monocoronal tiling with respect to direct congruence is crystallographic, whereas any monocoronal tiling with respect to congruence (reflections allowed) is either crystallographic or it has a one-dimensional translation group. Furthermore, bounds on the number of the dimensions of the translation group of monocoronal tilings in higher dimensional Euclidean space are obtained.

Volume: Vol. 17 no.2
Section: Combinatorics
Published on: October 5, 2015
Submitted on: December 1, 2014
Keywords: Symmetry groups,Tilings,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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