On the Notions of Symmetry and Aperiodicity for Delone Sets

doi:10.3390/sym4040566

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

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On the Notions of Symmetry and Aperiodicity for Delone Sets

Michael Baake^1,* and Uwe Grimm²

¹ Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany ² Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK

* Author to whom correspondence should be addressed.

Received: 3 August 2012; in revised form: 25 September 2012 / Accepted: 28 September 2012 / Published: 10 October 2012

(This article belongs to the Special Issue Crystal Symmetry and Structure)

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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

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MDPI and ACS Style

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

AMA Style

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

Chicago/Turabian Style

Baake, Michael; Grimm, Uwe. 2012. "On the Notions of Symmetry and Aperiodicity for Delone Sets." Symmetry 4, no. 4: 566-580.

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