# Symmetry Space Group Diagram

I am doing an introductory course to Crystallography and I have found in the following web page: http://pd.chem.ucl.ac.uk/pdnn/symm3/sgmonoc.htm a guide for the elaboration of the diagrams of the spatial groups.

In this tutorial, they say the following: "The symmetry operator for the c-glide plane is of the form x,T-y,1/2+z, while the symmetry operator for the two-one screw axis is of the form T′-x,1/2+y,T′′-z. It is possible to show (using matrices) that the only values for T, T′, and T′′, which permit the symmetry operators to form a closed group, are 1/2, 0, and 1/2, respectively"

They could tell me how to calculate the values of T, T' and T'' using the matrices.

• Why, that's simple. Apply each operator twice and see where this gets you. – Ivan Neretin Aug 16 at 15:11
• Sorry, but I don't understand you – aprendiendo-a-programar Aug 16 at 15:23
• They say the symmetry operator has a certain form. What does that mean, if anything? I'll tell you what. It means that the operator grabs any point (x,y,z) and relocates it to certain other coordinates. Now I suggest looking at what happens if you apply the operator twice. – Ivan Neretin Aug 16 at 15:40
• But, I would like to know how to obtain the values of T, T', T'' through the use of matrices. – aprendiendo-a-programar Aug 16 at 15:41
• Take a huge whiteboard marker and write "Matrices" on your chair where you will be sitting while doing this. I think that will count as the use of matrices. Seriously, what is the point of using a specific instrument you don't really need? – Ivan Neretin Aug 16 at 15:49