{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:59:05Z","timestamp":1760241545175,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,5,14]],"date-time":"2018-05-14T00:00:00Z","timestamp":1526256000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["14-50-00005"],"award-info":[{"award-number":["14-50-00005"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The main goal of the local theory for crystals developed in the last quarter of the 20th Century by a geometry group of Delone (Delaunay) at the Steklov Mathematical Institute is to find and prove the correct statements rigorously explaining why the crystalline structure follows from the pair-wise identity of local arrangements around each atom. Originally, the local theory for regular and multiregular systems was developed with the assumption that all point sets under consideration are     ( r , R )    -systems or, in other words, Delone sets of type     ( r , R )     in d-dimensional Euclidean space. In this paper, we will review the recent results of the local theory for a wider class of point sets compared with the Delone sets. We call them t-bonded sets. This theory, in particular, might provide new insight into the case for which the atomic structure of matter is a Delone set of a \u201cmicroporous\u201d character, i.e., a set that contains relatively large cavities free from points of the set.<\/jats:p>","DOI":"10.3390\/sym10050159","type":"journal-article","created":{"date-parts":[[2018,5,15]],"date-time":"2018-05-15T03:29:34Z","timestamp":1526354974000},"page":"159","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Local Theory for Regular Systems in the Context of t-Bonded Sets"],"prefix":"10.3390","volume":"10","author":[{"given":"Mikhail","family":"Bouniaev","sequence":"first","affiliation":[{"name":"University of Texas Rio Grande Valley, Brownsville, TX 78520, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nikolay","family":"Dolbilin","sequence":"additional","affiliation":[{"name":"Steklov Mathematical Institute of Russian Academy of Sciences, Moscow 119991, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,14]]},"reference":[{"key":"ref_1","unstructured":"Feynmann, R., Leighton, R., and Sands, M. 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