Hi all, I'm sorry to be making my first post a question but here goes anyway.

I'm just trying to get my head around crystallography and its conventions. I'm not liking it at all! I really hate to feel stupid, and this particular problem is driving me crazy. It's probably so simple but without a good explanation, staring at diagrams the past hour has just left me confused. I've also come across conflicting ideas, which really doesn't help

Anyway I'll jump right into it - I've got an example of a space group diagram:

I can see that there are what I believe to be symmetry operators (red circles in the box), with the object of origin in the bottom left corner (the empty circle with a positive sign, bottom left inside the box). To the right of the space group diagram are the coordinates to those symmetry operators, with the origin coordinates in blue.

What I am really not getting is the correlation to the points and those coordinates. I completely understand that the origin would be x, y, z. However, my attempts at getting the other coordinates seem to never work. I get why the origin is being repeated as it is. Let me take the next object above the origin, which I believe to be a translation of the origin in a glide plane (shown as the dotted line) parallel to the z axis.

What I would write down as its coordinates would be: x , 1/2 + y, 1/2 + z

Why? - because there has been no movement along the x axis.

- there has been a shift half way up the unit cell along the y axis (and therefore I think it is 1/2 + y)

- I wont lie, I'm saying it's 1/2 + z because it shows that on the diagram.

Looking at the supplied coordinates, I can see that this set of coordinates do not fit in, and I'm quite obviously wrong. I think that if I can't understand this, the more complicated things get the further frustration will build. So please, if anyone can educate me as to how to derive coordinates from these points, and explain where I'm going wrong - you'd make my day (well night, as it's nearly 1am and I've made no progress in my work!).

Thanks a lot.