Construct the little group based on Wyckoff positions.

[hongyi-zhao]

According to my understanding, the little group in nature is the site symmetry group in reciprocal space. On the other hand, the site symmetry group and the Wyckoff position has the following relationship:

In crystallography, a Wyckoff position is a point belonging to a set of points for which site symmetry groups are conjugate subgroups of the space group.

So, I think it should be possible to build/construct the little group based on Wyckoff positions.

Any hints/comments/corrections on this idea will be appreciated.

N.B.: I also noticed the related - to some extent, if not all - application here.

Regards,
Zhao

[lan496]

I don't fully understand the connection between the little group you mentioned and Wyckoff positions.
But it seems a reciprocal-space group will help formalize your problem.

• http://scripts.iucr.org/cgi-bin/paper?S205327331303091X
• https://it.iucr.org/Bb/ch1o5v0001/ch1o5.pdf

[hongyi-zhao]

I don't fully understand the connection between the little group you mentioned and Wyckoff positions.

I mean that the little group in nature is the site symmetry group in the reciprocal-space group.

• https://it.iucr.org/Bb/ch1o5v0001/ch1o5.pdf

Here is an updated version of the book International Tables for Crystallography Volume B: Reciprocal space (Edition: 4), and the above paper is excerpted from this volume.