{"title":"Isogonal embeddings of interwoven and self-entangled honeycomb (hcb) nets and related interpenetrating primitive cubic (pcu) nets.","authors":"Michael O'Keeffe, Michael M J Treacy","doi":"10.1107/S2053273323008495","DOIUrl":null,"url":null,"abstract":"<p><p>Two- and three-periodic vertex-transitive (isogonal) piecewise-linear embeddings of self-entangled and interwoven honeycomb nets are described. The infinite families with trigonal symmetry and edge transitivity (isotoxal) are particularly interesting as they have the Borromean property that no two nets are directly linked. These also lead directly to infinite families of interpenetrating primitive cubic nets (pcu) that are also vertex- and edge-transitive and have embeddings with 90° angles between edges.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"560-569"},"PeriodicalIF":1.9000,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Crystallographica Section A: Foundations and Advances","FirstCategoryId":"1","ListUrlMain":"https://doi.org/10.1107/S2053273323008495","RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/10/26 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Two- and three-periodic vertex-transitive (isogonal) piecewise-linear embeddings of self-entangled and interwoven honeycomb nets are described. The infinite families with trigonal symmetry and edge transitivity (isotoxal) are particularly interesting as they have the Borromean property that no two nets are directly linked. These also lead directly to infinite families of interpenetrating primitive cubic nets (pcu) that are also vertex- and edge-transitive and have embeddings with 90° angles between edges.
期刊介绍：
Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials.
The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial.
The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.
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