I have a question regarding space group notation, when generating the equivalent positions.
For example the space group P21
This is a monoclinic system, therefore the first operator is perpendicular to a, the second to b and the third to c (the first and third operators being 1 in this case, i.e nothing). But how do I handle 21
/m ? I know what those symbols mean, it's a screw axis and a mirror plane but how do I use them. Do I first generate positions from the screw axis, and then apply the mirror plane to those 2 generated positions? I tried this but it did not seem to be correct when controlling against space group data.
Starting from position x,y,z a 21
screw axis generates the position -x, 1/2+y, -z.
If applying a mirror plane perpendicular to those two positions you get: x, -y, z and -x, 1/2-y, -z. But this doesn't fit with the table.
I also have a question regarding tetragonal space groups, where the symmetry operators are applied perpendicular to c, a and finally ab. I understand what perpendicular to a and c means, but ab? I cant visualise this, something perpendicular to two different axis.