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从 NTN =T这一晶体学的普遍公式出发 ,推导出在三维空间中度量张量矩阵T有四个算术不等价类 ,即T1 =10 00 100 0 1,T2 =2 1012 00 0 2,T3=2 1112 1112,T4=3- 1- 1- 13- 1- 1- 13,而T1 ,T3,T4属几何等价类 ,故几何不等价类只有T1 及T2 .根据 NT1 N =T1 及 NT2 N =T2 求出三维晶体学的两个极大有限群分别为 48阶及 2 4阶 ,它们对应于两个晶体学点群 ,其他三十个点群则可通过母子群网求出
Starting from the general formula of crystallography of NTN = T, it is deduced that there are four arithmetic inequalities in metric tensor matrix T in three-dimensional space, namely T1 = 10 00 100 0 1, T2 = 2 1012 00 0 2, T3 = 2 1112 1112, T4 = 3- 1- 1- 13- 1- 1- 13, and T1, T3, T4 belong to geometric equivalence class, so the geometric inequalities have only T1 and T2. According to NT1 N = T1 And NT2 N = T2, the two maximal finite groups of three-dimensional crystallography are respectively 48 order and 24 order, which correspond to two crystallographic point groups. The other thirty point groups can be obtained by the mother-son group network