{"title":"晶体结构中多面体和分子层的平面层叠：结构类 cm，Z = 2(m)","authors":"K. G. Seravkin, K. A. Potekhin, A. M. Banaru","doi":"10.3103/S0027131424010097","DOIUrl":null,"url":null,"abstract":"<p>Lattice tilings of a plane into polyominoes are constructed for <i>N</i> from 3 to 12, where <i>N</i> is the order of the packing space. A total of 5191 symmetrically independent lattice tilings of the plane with one polyomino in a reduced (primitive) cell are obtained, among which 122 variants belong to the structural class (SC) <i>cm</i>, <i>Z</i> = 2(<i>m</i>), with a rectangular conventional (centered) unit cell. Chain tilings of the plane are derived, for which both the SC and structural subclass (SSC) are identified. The results of the analysis of the lattice tilings of a plane into polyominoes are illustrated with examples of real molecular layers in crystal structures.</p>","PeriodicalId":709,"journal":{"name":"Moscow University Chemistry Bulletin","volume":"79 1","pages":"14 - 20"},"PeriodicalIF":0.7000,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lattice Tilings of a Plane into Polyominoes and Molecular Layers in Crystal Structures: Structural Class cm, Z = 2(m)\",\"authors\":\"K. G. Seravkin, K. A. Potekhin, A. M. Banaru\",\"doi\":\"10.3103/S0027131424010097\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Lattice tilings of a plane into polyominoes are constructed for <i>N</i> from 3 to 12, where <i>N</i> is the order of the packing space. A total of 5191 symmetrically independent lattice tilings of the plane with one polyomino in a reduced (primitive) cell are obtained, among which 122 variants belong to the structural class (SC) <i>cm</i>, <i>Z</i> = 2(<i>m</i>), with a rectangular conventional (centered) unit cell. Chain tilings of the plane are derived, for which both the SC and structural subclass (SSC) are identified. The results of the analysis of the lattice tilings of a plane into polyominoes are illustrated with examples of real molecular layers in crystal structures.</p>\",\"PeriodicalId\":709,\"journal\":{\"name\":\"Moscow University Chemistry Bulletin\",\"volume\":\"79 1\",\"pages\":\"14 - 20\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Moscow University Chemistry Bulletin\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.3103/S0027131424010097\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow University Chemistry Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.3103/S0027131424010097","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
摘要 构建了从 3 到 12 个 N 的平面多角形网格倾斜图，其中 N 是堆积空间的阶数。总共得到了 5191 个对称独立的、在缩小（原始）单元中有一个多面体的平面点阵，其中 122 个变体属于结构类（SC）cm，Z = 2(m)，具有矩形常规（居中）单元格。推导出了平面的链状倾斜，并确定了 SC 和结构亚类（SSC）。以晶体结构中的实际分子层为例，说明了将平面的晶格倾斜分析为多面体的结果。
Lattice Tilings of a Plane into Polyominoes and Molecular Layers in Crystal Structures: Structural Class cm, Z = 2(m)
Lattice tilings of a plane into polyominoes are constructed for N from 3 to 12, where N is the order of the packing space. A total of 5191 symmetrically independent lattice tilings of the plane with one polyomino in a reduced (primitive) cell are obtained, among which 122 variants belong to the structural class (SC) cm, Z = 2(m), with a rectangular conventional (centered) unit cell. Chain tilings of the plane are derived, for which both the SC and structural subclass (SSC) are identified. The results of the analysis of the lattice tilings of a plane into polyominoes are illustrated with examples of real molecular layers in crystal structures.
期刊介绍：
Moscow University Chemistry Bulletin is a journal that publishes review articles, original research articles, and short communications on various areas of basic and applied research in chemistry, including medical chemistry and pharmacology.
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