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arXiv math-ph/0310026math-phmath.GRmath.MP
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二十面体多分量模型集

Icosahedral multi-component model sets

Nicolae Cotfas

摘要:

对于任何二十面体簇C,可以用条带投影法定义C的互穿副本的准周期堆积Q,其中大多数副本仅部分占据。我们证明了当C的向量的坐标属于二次域Q[ \sqrt{5} ]时,超空间的维数可以降低,即Q可以用一个6维超空间重新定义为一个多分量模型集.

英文摘要:

A quasiperiodic packing Q of interpenetrating copies of C, most of them only partially occupied, can be defined in terms of the strip projection method for any icosahedral cluster C. We show that in the case when the coordinates of the vectors of C belong to the quadratic field Q[\sqrt{5}] the dimension of the superspace can be reduced, namely, Q can be re-defined as a multi-component model set by using a 6-dimensional superspace.

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