Local Theory of Regular Systems and Delone Sets

N. P. Dolbilin

Informatics and Automation, Geometry, Topology, and Mathematical Physics, Tome 325 (2024), pp. 129-145

Résumé

We survey the results of the local theory of regular systems that are related to estimating the regularity radius. We also discuss recent results on local groups in arbitrary Delone sets in the plane and in the three-dimensional space, including new theorems and conjectures generalizing the classical statement on the absence of fivefold rotations in lattices.

Détail

Keywords: crystallographic group, regular system, multiregular system, cluster, local group, regularity radius.
Mots-clés : Delone (Delaunay) set

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