FMF - Friends of Minerals Forum, discussion and message board

[prcantos]

Maybe I have found an answer to one of my previous questions: why are we using some dashed-lines matching symmetry elements which don't belong to the consider symmetry group? If they don't belong to the group they wouldn't be used to classify the forms.

The answer is related to 'Wyckoff positions' and 'crystallographic orbits'. These are concepts that appear in the study of space groups and can be transferred to point groups.

I haven't studied space groups before, but I am doing it now. I will tell you what I learn.

[prcantos]

Meanwhile I add a new example of the matricial calculations of the forms for the group G=4/m, with the same notation and procedures. The columns in the matrix A are the images of (h,k,l) by identity, the 4-fold Z-axis rotation ρ and the XY-mirror symmetry σ.