晶体点群和SO(3),O(3)群的关系

The Relation Between Symmetrical Point Groups and SO(3),O(3)Groups

第一类和第二类晶体点群共有32种[1],但为什么不会有其它的存在,以及这些点群和全旋转群SO（3）,正交群O（3）的生成关系还没有相关论述,本文从群的生成关系出发,解释为什么点群只有那么多,这些点群和全旋转群SO（3）,正交群O（3）的关系,以及可能具有点群对称性的正多面体结构.

There are altogether 32 sorts of first class and second class crystal point groups, but why don't other groups exist and What's the relation between the point groups and SO (3), O (3) groups have not been discussed. In this paper, a interpretation is given that why there are only 32 sorts of point groups and the relation between the point groups and SO (3), O (3) groups according to the ball triangular equation. In the back part, the possible regular polyhedrons with the point groups' symmetry is discussed.