多壳层团簇的准周期堆积生成算法
Algorithm for Generating Quasiperiodic Packings of Multi-Shell Clusters
摘要：
准晶物理学中的许多数学模型都是基于四维、五维或六维超空间中用条带投影法得到的平面或空间的平铺。我们提出了一些数学结果，使人们可以使用这种非常优雅的方法在空间的维度更高，并直接产生准周期包装的多壳层集群。我们表明，在一个二维的情况下（resp。三维）集群，我们必须只计算三阶的行列式（分别为）。四），独立于我们使用的超空间的维度。基于我们的数学结果的计算机程序是非常有效的。例如，我们可以在31维空间中利用条带投影方法很容易地生成三壳层二十面体团簇（二十面体+十二面体+二十半十二面体）的准周期堆积（在个人计算机上几分钟内获得数百个点）。
英文摘要：
Many of the mathematical models used in quasicrystal physics are based on tilings of the plane or space obtained by using strip projection method in a superspace of dimension four, five or six. We present some mathematical results which allow one to use this very elegant method in spaces of dimension much higher and to generate directly quasiperiodic packings of multi-shell clusters. We show that in the case of a two-dimensional (resp. three-dimensional) cluster we have to compute only determinants of order three (resp. four), independently of the dimension of the superspace we use. The computer program based on our mathematical results is very efficient. For example, we can easily generate quasiperiodic packings of three-shell icosahedral clusters (icosahedron + dodecahedron + icosidodecahedron) by using strip projection method in a 31-dimensional space (hundreds of points are obtained in a few minutes on a personal computer).
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