Question

I can't understand how to draw 3D point groups.

Especially, three rotational axes like 222 322 422 622 233 432.

If I understand upper case, after case could understand like mmm m3m

So, I want to know how to draw 222 233 432 very detail

Answer 1

I am sorry I could not draw the point group by hand as its becoming nasty. I am uploading the picture that my professor has taught.

As I have derived the angle so we have the respective operation at a distance 54 degree 44 min. Also, I have given you the settings for a cubic. The 2nd setting is 111 which makes the figure complicated.

In case of 23 first is 180 rotation along z axis the 90 degree rotation along 111 direction which gives the figure below

In case of 432 ,The first case is 4 fold rotation along z-axis ,then 3 fold rotation along 111 direction which gives the figure

I understand that It's very difficult to grasp for the cubic point groups . So any doubt you can ask me ..