An original structural model for the description of icosahedral quasicrystals is proposed. This novel theoretical approach is based on a surface-stacking image of icosahedral quasicrystals and is in concert with the step-terrace morphology observed in many experimental investigations of real icosahedral surfaces. According to this model, the infinite icosahedral structure is constructed by stacking two arrangements of quasi-periodic surfaces along each of the 5-fold axis of the icosahedral symmetry. In this stacking order, the spacings between the layered surfaces are governed by Fibonacci sequence. The proposed model operates within the real physical (Euclidean) space and provides a direct three-dimensional visual representation of the icosahedral superstructure, which can be instrumental for conducting different modes of experimentations, analyses, and fabrication strategies; eliminating a major roadblock for researchers especially outside the fields of crystallography and material science. More importantly, understanding the long-range surface-stacking logic of the icosahedral structure will hopefully provide a deeper understanding of the structure of quasicrystals at an atomic scale and help achieve improved control over material compositions and structure.

中文翻译：

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二十面体准晶的表面堆叠结构模型

提出了用于描述二十面体准晶的原始结构模型。这种新颖的理论方法基于二十面体准晶的表面堆叠图像，并且与在真实二十面体表面的许多实验研究中观察到的阶梯形形态一致。根据该模型，无限二十面体结构是通过沿二十面体对称性的 5 重轴中的每一个堆叠准周期表面的两个排列来构建的。在此堆叠顺序中，分层表面之间的间距由斐波那契数列控制。所提出的模型在真实的物理（欧几里得）空间内运行，并提供了二十面体上层结构的直接三维视觉表示，这有助于进行不同的实验模式，分析和制造策略；消除了研究人员的主要障碍，尤其是在晶体学和材料科学领域之外。更重要的是，了解二十面体结构的长程表面堆叠逻辑将有望在原子尺度上更深入地了解准晶体的结构，并有助于改善对材料成分和结构的控制。