Minimal-transitivity finite tangles and catenated polyhedra.

IF 2.1 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2026-03-01 Epub Date: 2026-01-22 DOI:10.1107/S2053273326000252

Michael O'Keeffe, Michael M J Treacy

引用次数: 0

Abstract

Tangles are defined as embeddings of connected graphs that contain knots and/or links as substructures. We enumerate and describe piecewise-linear embeddings of cubic and icosahedral tangles and linked polyhedra with transitivity [1 2]; that is, with one kind of vertex (all related by symmetry) and two kinds of edge. There are eight families of catenated polyhedra and ten families of tangles. For each family, we only describe the members with the largest girth, where girth is defined as the ratio of the shortest distance between edges with no shared vertices to the length of the longest edge.

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最小传递性有限缠结和链状多面体。

缠结被定义为包含结和/或链接作为子结构的连接图的嵌入。我们列举并描述了具有传递性的立方和二十面体缠结和连接多面体的分段线性嵌入[1 2]；也就是说，有一种顶点（都是对称的）和两种边。链状多面体有八科，缠结多面体有十科。对于每个族，我们只描述具有最大周长的成员，其中周长定义为没有共享顶点的边之间的最短距离与最长边的长度之比。

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.