Isogonal embeddings of interwoven and self-entangled honeycomb (hcb) nets and related interpenetrating primitive cubic (pcu) nets.

IF 1.9 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2023-11-01 Epub Date: 2023-10-26 DOI:10.1107/S2053273323008495

Michael O'Keeffe, Michael M J Treacy

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.

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交织自纠缠蜂窝（hcb）网络和相关的互穿原始立方体（pcu）网络的等角嵌入。

描述了自纠缠和交织蜂窝网的二周期和三周期顶点传递（等角）分段线性嵌入。具有三角对称性和边传递性（isotroxal）的无限族特别有趣，因为它们具有没有两个网直接连接的Borromean性质。这些也直接导致了无限族的互穿原始三次网（pcu），它们也是顶点和边传递的，并且在边之间具有90°角的嵌入。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Crystallographica Section A: Foundations and Advances CHEMISTRY, MULTIDISCIPLINARYCRYSTALLOGRAPH-CRYSTALLOGRAPHY

CiteScore

2.60

自引率

11.10%

发文量

419

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.