Dnd点群的几点释疑

Interpretation on Point Group of Dnd

Point group in crystallography is one of the important subjects in structural chemistry.Some topics are very difficult to understand.To name a few, why does point group of D_2d belong to tetragonal? Why are D_4d and D_6d not included in 32 kinds of crystallographic point groups? The two questions are easy to answer if we understand the following topic:for the D_nd point group, when n is odd, it contains an I_n symmetry axis; when n is even, it contains an I_2n symmetry axis.In this work, graphic method and matrix method are adopted to clarify why the D_nd point group includes an S_2n axis, and thus give explanations that D_2d belongs to tetragonal as well as D_4d and D_6d are not included in 32 kinds of crystallographic point groups.