晶体学与准晶体学点群的母子群关系

依据群论，得出了准晶体学点群的直积或半直积推导算式；依据结晶学理论，绘出了五角、八角、十角和十二角晶系各点群的极赤投影图.据此推导出了每一个准晶体学点群的全部最大子群，从而推导并绘制出了三维晶体学和准晶体学点群之间的母子群关系(60个点群的“家谱”).该“家谱”以最大子群链的图解形式直观地给出了每个点群的最小母群和最大子群. 关键词： 准晶体 晶体 点群 最大子群 最小母群 群链

Subgroups and supergroups of crystallographic and quasi-crystallographic point groups

The direct products and semidirect products of quasi-crystallographic point groups, were derived from group theory. According to crystallography theory, the stereographic projection of pentagonal system, octagonal system, decagonal system and dodecagonal system, were derived and drawn. Basing upon them, all maximal subgroups of each quasi-crystallographic point group were derived and drawn. As a result, subgroups and supergroups of the three-dimensional crystallographic and quasi-crystallographic point groups (the ‘family tree' of sixty point groups) were derived and depicted in drawing. In the ‘family tree', the minimal supergroups and maximal subgroups of sixty point groups were illustrated in detail in the form of maximal subgroup chains.