{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:35:37Z","timestamp":1760243737220,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2012,10,10]],"date-time":"2012-10-10T00:00:00Z","timestamp":1349827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/sym4040566","type":"journal-article","created":{"date-parts":[[2012,10,10]],"date-time":"2012-10-10T20:42:28Z","timestamp":1349901748000},"page":"566-580","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On the Notions of Symmetry and Aperiodicity for Delone Sets"],"prefix":"10.3390","volume":"4","author":[{"given":"Michael","family":"Baake","sequence":"first","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Bielefeld, Postfach 100131, 33501 Bielefeld, Germany"}]},{"given":"Uwe","family":"Grimm","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK"}]}],"member":"1968","published-online":{"date-parts":[[2012,10,10]]},"reference":[{"key":"ref_1","unstructured":"Schwarzenberger, R.L.E. 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