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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.
According to the theory of group, the direct or semidirect product formula of quasicrystal point group is deduced. According to the theory of crystallography, the extreme red projection picture of each point group of pentagonal, octagonal, decagonal and twelve-angle crystal system According to this, all the largest subgroups of each quasi-crystallographic point group are deduced, and then the relationship between mother and child (the “genealogy” of 60 point groups) is deduced and drawn between three-dimensional crystallographic and quasi-crystallographic point groups The “genealogy” intuitively gives the minimum and maximum subgroups of each point group in graphical form of the largest subgroup chain.