Octagonal tilings with three prototiles.

IF 2.1 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2026-05-01 Epub Date: 2026-04-10 DOI:10.1107/S2053273326002767

April Lynne Say-Awen, Sam Coates

引用次数: 0

Abstract

Motivated by theoretically and experimentally observed structural phases with octagonal symmetry, we introduce families of octagonal tilings composed of three prototiles. These tilings are defined by substitution rules with inflation factors δ^(m,n) = m + n(1 + √2), where m, n are nonnegative integers. We consider the cases (m, n) = (1, 1), (2, 2), (1, 2), (3, 2) and describe their basic properties. In addition, we discuss variants of the first three cases, and for (1, 1) we derive the relative frequencies of the vertex stars.

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带有三个原型的八角形瓷砖。

根据理论和实验观察到的具有八角形对称的结构相，我们引入了由三个原始瓷砖组成的八角形瓷砖族。这些平铺由膨胀因子δ(m,n) = m + n（1 +√2）的替换规则定义，其中m，n为非负整数。我们考虑(m, n) =(1,1),(2,2),(1,2),（3,2）的情况，并描述它们的基本性质。此外，我们讨论了前三种情况的变体，并对（1,1）导出了顶点星的相对频率。

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.