Symmetries of monocoronal tilings

Authors

Dirk Frettlöh
Alexey Garber, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

2015

Abstract

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.

Comments

Copyright 2015 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France

Recommended Citation

Dirk Frettlöh, Alexey Garber. Symmetries of Monocoronal Tilings. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no.2 (2), pp.203-234. ⟨hal-01349057⟩

Publication Title

Discrete Mathematics and Theoretical Computer Science