Fujita Nobuhisa
Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan.
Acta Crystallogr A. 2009 Sep;65(Pt 5):342-51. doi: 10.1107/S0108767309025008. Epub 2009 Jul 30.
A general construction principle for the inflation rules for decagonal quasiperiodic tilings is proposed. The prototiles are confined to be polygons with unit edges. An inflation rule for a tiling is the combination of expansion and division of the tiles, where the expanded tiles can be divided arbitrarily as long as the set of prototiles is maintained. A certain kind of point decoration process turns out to be useful for the identification of possible division rules. The method is capable of generating a broad range of decagonal tilings, many of which are chiral and have atomic surfaces with fractal boundaries. Two new families of decagonal tilings are presented; one is quaternary and the other ternary. The properties of the ternary tilings with rhombic, pentagonal and hexagonal prototiles are investigated in detail.
提出了十边形准周期平铺膨胀规则的一般构建原则。原瓷砖被限制为具有单位边长的多边形。平铺的膨胀规则是瓷砖的扩展和划分的组合，只要保持原瓷砖集，扩展后的瓷砖可以任意划分。事实证明，某种点装饰过程对于识别可能的划分规则很有用。该方法能够生成广泛的十边形平铺，其中许多是手性的，并且具有带有分形边界的原子表面。给出了两个新的十边形平铺族；一个是四元的，另一个是三元的。详细研究了具有菱形、五边形和六边形原瓷砖的三元平铺的性质。
