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Symmetry 2012, 4(4), 566-580; doi:10.3390/sym4040566
Article

On the Notions of Symmetry and Aperiodicity for Delone Sets

1,*  and 2
Received: 3 August 2012 / Revised: 25 September 2012 / Accepted: 28 September 2012 / Published: 10 October 2012
(This article belongs to the Special Issue Crystal Symmetry and Structure)
Download PDF [244 KB, uploaded 10 October 2012]

Abstract

Non-periodic systems have become more important in recent years, both theoretically and practically. Their description via Delone sets requires the extension of many standard concepts of crystallography. Here, we summarise some useful notions of symmetry and aperiodicity, with special focus on the concept of the hull of a Delone set. Our aim is to contribute to a more systematic and consistent use of the different notions.
Keywords: Delone sets; tilings; symmetry; aperiodicity Delone sets; tilings; symmetry; aperiodicity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Baake, M.; Grimm, U. On the Notions of Symmetry and Aperiodicity for Delone Sets. Symmetry 2012, 4, 566-580.

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