{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,14]],"date-time":"2025-01-14T05:17:36Z","timestamp":1736831856688,"version":"3.33.0"},"reference-count":19,"publisher":"International Union of Crystallography (IUCr)","issue":"5","license":[{"start":{"date-parts":[[2015,8,28]],"date-time":"2015-08-28T00:00:00Z","timestamp":1440720000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/journals.iucr.org\/services\/copyrightpolicy.html"},{"start":{"date-parts":[[2015,8,28]],"date-time":"2015-08-28T00:00:00Z","timestamp":1440720000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/journals.iucr.org\/services\/copyrightpolicy.html#TDM"}],"content-domain":{"domain":["iucr.org","wiley.com","iucrj.org"],"crossmark-restriction":true},"short-container-title":["Acta Crystallogr A Found Adv","Acta Crystallogr A","Acta Crystallogr A Found Crystallogr","Acta Cryst A","Acta Cryst A Found Adv","Acta Cryst Sect A","Acta Cryst Sect A Found Adv","Acta Crystallogr Sect A","Acta Crystallogr Sect A Found Adv","Acta Crystallogr Sect A Found Crystallogr"],"published-print":{"date-parts":[[2015,9,1]]},"abstract":"<jats:p>In the study of pattern formation in symmetric physical systems, a three-dimensional structure in thin domains is often modelled as a two-dimensional one. This paper is concerned with functions in {\\bb R}^{3} that are invariant under the action of a crystallographic group and the symmetries of their projections into a function defined on a plane. A list is obtained of the crystallographic groups for which the projected functions have a hexagonal lattice of periods. The proof is constructive and the result may be used in the study of observed patterns in thin domains, whose symmetries are not expected in two-dimensional models, like the black-eye pattern.<\/jats:p>","DOI":"10.1107\/s2053273315012905","type":"journal-article","created":{"date-parts":[[2015,8,27]],"date-time":"2015-08-27T12:07:07Z","timestamp":1440677227000},"page":"549-558","update-policy":"https:\/\/doi.org\/10.1107\/cm_01","source":"Crossref","is-referenced-by-count":1,"title":["Hexagonal projected symmetries"],"prefix":"10.1107","volume":"71","author":[{"given":"Juliane F.","family":"Oliveira","sequence":"first","affiliation":[]},{"given":"Sofia B. S. 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