3-Periodic weavings: piecewise linear embeddings of symmetric structures.

IF 1.8 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2025-09-01 Epub Date: 2025-07-07 DOI:10.1107/S2053273325004802

Michael O'Keeffe, Michael M J Treacy

引用次数: 0

Abstract

We provide a systematic account using symmetry and coordinates to explore symmetric (vertex- and edge-transitive) 3-periodic weavings of piecewise linear threads. The dia-w graph, derived from the diamond structure, generates an infinite family of supersymmetric 3-periodic thread weaves - a unique property shared only with the 2-periodic sql-w family of fabric weaves. Additionally, we describe a selection of symmetric 3-periodic, 3-coordinated weavings related to the srs graph and a supersymmetric Borromean weave of hcb graphs.

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周期性编织：对称结构的分段线性嵌入。

我们提供了一个系统的帐户，使用对称和坐标来探索对称（顶点和边缘传递）分段线性线的3周期编织。从菱形结构中导出的dia-w图生成了一个无限的超对称3周期线织族，这是只有2周期sql-w家族织物织族才具有的独特性质。此外，我们描述了与srs图相关的对称3周期，3协调编织的选择和hcb图的超对称Borromean编织。

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.