二十面体准点阵的切割投影法构造

The Cut-and-Project Construction for the Icosahedral Quasilattice

用切割投影法研究了二十面体准点阵结构。根据投影操作矩阵导出了二十面体准点阵的整数坐标 ,在此基础上计算出了它的三维阵点坐标 ,并构造出了二十面体准点阵结构的几何模型。由经典的对称理论 ,不同取向的对称轴间存在着组合规律 ,在两个以上方向具有非晶体学对称轴的点群只可能是二十面体型的 2 35或 5 - 3- 2 /m。由此构建的二十面体准点阵结构模型有六个 5 - 次轴 ,十个 3- 次轴和十五个 2次轴 ,具有同正二十面体一样的点对称群 5 - 3- 2 /m。

This paper deals with concerns the construction of an icosahedral quasilattice by the cut and project method.For this three dimensional quasilattice,the autor has derived the integral coordinates of the lattice points in terms of the operating matrices and computed its three dimensional coordinates.On the basis of the computation,he has constructed its geometrical model.With respect to calssical symmetry theory,there exists combination rule between different symmetry axes,and 235 or 5-3-2/m is the only possible point group for the non crystallographic symmetry axes above two dimensions .It is shown that the constructed model has six 5- axes,ten 3- axes and fifteen 2 axes.It has the same point group as an icosahedron,namely 5-3-2/m.