the 32 crystallographic point groups

例句：

1. 1. The study of 32 crystallographic point groups is crucial for understanding the structure of materials.
   研究32种晶体学点群对于理解材料的结构至关重要。
2. 2. In crystallography, these point groups are used to describe how atoms interact within a crystal.
   在晶体学中，这些点群用于描述原子在晶体内相互作用的方式。
3. 3. The discovery of new crystallographic point groups has led to significant advancements in material science.
   新发现晶体学点群的进展在材料科学领域产生了重大进步。