{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,5]],"date-time":"2026-11-05T10:29:23Z","timestamp":1793874563406,"version":"4.6.1"},"reference-count":11,"publisher":"International Union of Crystallography (IUCr)","issue":"6","license":[{"start":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T00:00:00Z","timestamp":1791763200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/journals.iucr.org\/services\/copyrightpolicy.html"},{"start":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T00:00:00Z","timestamp":1791763200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/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"],"accepted":{"date-parts":[[2026,9,26]]},"published-print":{"date-parts":[[2026,11,1]]},"abstract":"<jats:p>\n                    The problem of how to split the 3D space into two identical triply periodic but disjointed objects, using a contiguous surface of minimal area, was solved by Hermann Schwarz. His minimal surface, later called P after the (two) underlying primitive cubic lattices used for the frameworks of the two labyrinths, has a formidable analytical definition based on elliptic functions and Weierstrass\u2013Enneper integrals, although a simple trigonometric approximation also exists. Here, we derive the Schwarz minimal P surface from close tiling of the 3D space with regular polyhedra. This approach clearly exposes the\n                    <jats:italic>Im<\/jats:italic>\n                    <jats:overline>3<\/jats:overline>\n                    <jats:italic>m<\/jats:italic>\n                    symmetry of this surface and provides a starting point for its iterative generation through the minimization of the area of its crystallographic asymmetric unit.\n                  <\/jats:p>","DOI":"10.1107\/s205327332601003x","type":"journal-article","created":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T13:45:36Z","timestamp":1791207936000},"page":"464-471","update-policy":"https:\/\/doi.org\/10.1107\/cm_01","source":"Crossref","is-referenced-by-count":0,"title":["On the symmetry properties and crystallographic generation of the Schwarz minimal P surface"],"prefix":"10.1107","volume":"82","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8806-9066","authenticated-orcid":true,"given":"Zbigniew","family":"Dauter","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1587-6489","authenticated-orcid":true,"given":"Mariusz","family":"Jaskolski","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04g6bbq64","id-type":"ROR","asserted-by":"publisher"}],"department":["Department of Crystallography, Faculty of Chemistry"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"329","published-online":{"date-parts":[[2026,10,12]]},"reference":[{"key":"uv5049_bb1","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1021\/cr00083a011","volume":"88","author":"Andersson","year":"1988","journal-title":"Chem. Rev."},{"key":"uv5049_bb2","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1039\/b618173b","volume":"136","author":"Cherezov","year":"2007","journal-title":"Faraday Discuss."},{"key":"uv5049_bb3","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1107\/S0108767313018370","volume":"69","author":"de Campo","year":"2013","journal-title":"Acta Cryst. A"},{"key":"uv5049_bb4","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1016\/S0009-2614(00)00453-X","volume":"322","author":"Gandy","year":"2000","journal-title":"Chem. Phys. Lett."},{"key":"uv5049_bb5","first-page":"2077","volume":"A354","author":"Karcher","year":"1996","journal-title":"Constr. Triply Period. Minim. Surf. Philos. Trans. R. Soc. London"},{"key":"uv5049_bb6","doi-asserted-by":"crossref","first-page":"14532","DOI":"10.1073\/pnas.93.25.14532","volume":"93","author":"Landau","year":"1996","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"uv5049_bb7","first-page":"346","volume":"85","author":"Lord","year":"2003","journal-title":"Period. Minim. Surf. Cubic Symmetry. Curr. Sci."},{"key":"uv5049_bb8","unstructured":"Schoen, A. H. (1970). Infinite Periodic Minimal Surfaces Without Self-Intersections. NASA Technical Report TN D-5541. Washington DC, USA."},{"key":"uv5049_bb9","unstructured":"Schwarz, H. A. (1865). \u00dcber minimalfl\u00e4chen. Monatsber. Berlin Akad."},{"key":"uv5049_bb10","doi-asserted-by":"crossref","unstructured":"Schwarz, H. A. (1890). Gesammelte Mathematische Abhandlungen. Berlin: Julius Springer.","DOI":"10.1007\/978-3-642-50665-9"},{"key":"uv5049_bb11","doi-asserted-by":"crossref","first-page":"D489","DOI":"10.1093\/nar\/gkaf1187","volume":"54","author":"Vallat","year":"2026","journal-title":"Nucleic Acids Res."}],"container-title":["Acta Crystallographica Section A Foundations and Advances"],"original-title":[],"link":[{"URL":"https:\/\/journals.iucr.org\/a\/issues\/2026\/06\/00\/uv5049\/uv5049.pdf","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.iucr.org\/a\/issues\/2026\/06\/00\/uv5049\/uv5049.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,11,5]],"date-time":"2026-11-05T10:01:20Z","timestamp":1793872880000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.iucr.org\/paper?S205327332601003X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,12]]},"references-count":11,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2026,11]]}},"alternative-id":["S205327332601003X"],"URL":"https:\/\/doi.org\/10.1107\/s205327332601003x","relation":{"is-supplemented-by":[{"id-type":"doi","id":"10.1107\/S205327332601003X\/uv5049sup1.pdf","asserted-by":"subject"}]},"ISSN":["2053-2733"],"issn-type":[{"value":"2053-2733","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,12]]},"assertion":[{"value":"Acta Crystallographica Section A: Foundations and Advances","order":0,"name":"journal","label":"Publication","explanation":{"URL":"https:\/\/journals.iucr.org\/a"},"group":{"name":"general","label":"General"}},{"value":"research papers","order":1,"name":"content_type","label":"Content type","explanation":{"URL":"https:\/\/journals.iucr.org\/a\/services\/notesforauthors.html"},"group":{"name":"general","label":"General"}},{"value":"Available","URL":"https:\/\/scripts.iucr.org\/cgi-bin\/citedin?uv5049","order":2,"name":"article_metrics","label":"Article metrics","group":{"name":"general","label":"General"}},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"7 June 2026","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication history"}},{"value":"26 September 2026","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication history"}},{"value":"12 October 2026","order":2,"name":"published_online","label":"Published online","group":{"name":"publication_history","label":"Publication history"}},{"value":"This article has supporting information","name":"supplementary_materials","label":"Supplementary materials","explanation":{"URL":"https:\/\/scripts.iucr.org\/cgi-bin\/sendsup?uv5049"}},{"value":"\u00a9 Dauter and Jaskolski","order":0,"name":"copyright","label":"Copyright","explanation":{"URL":"https:\/\/journals.iucr.org\/services\/copyrightpolicy.html"},"group":{"name":"copyright_and_licensing","label":"Copyright and licencing"}},{"value":"IUCr licence to publish","order":1,"name":"license","label":"Licence","explanation":{"URL":"https:\/\/journals.iucr.org\/copyright\/licencetopublish.html"},"group":{"name":"copyright_and_licencing","label":"Copyright and licencing"}}]}}