Symmetries of Monocoronal Tilings

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.
Type de document :
Article dans une revue
Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no.2 (2), pp.203-234
Liste complète des métadonnées

Littérature citée [10 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01349057
Contributeur : Coordination Episciences Iam <>
Soumis le : mardi 26 juillet 2016 - 16:47:01
Dernière modification le : jeudi 7 septembre 2017 - 01:03:44

Fichier

2737-9791-1-PB.pdf
Accord explicite pour ce dépôt

Identifiants

  • HAL Id : hal-01349057, version 1

Collections

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〉

Partager

Métriques

Consultations de la notice

30

Téléchargements de fichiers

215