# Pncn space group diagram

I'm trying to make a diagram of the Pncn space group.

Firstly, I know that this space group belongs to the orthorhombic system and derives from the point group (2/m 2/m 2/m).

Therefore, although the abbreviated notation does not appear, this spatial group also has binary axes (which may be normal or helical).

We also know that the multiplicity of the space group is 8. That is, there are 8 positions equivalent to (x,y,z). Next, we try to determine them:

1. By the translation of the primitive lattice: (x,y,z)
2. As the point group 2/m 2/m 2/m/m is centrosymmetric: (-x,-y,-z)
3. For the plane type "n" perpendicular to the axis "a": (-x, 1/2+y, 1/2+z)
4. By the plane type "c" perpendicular to the axis "b": (x, -y, 1/2+z)
5. By the plane type "n" perpendicular to the "c" axis: (1/2+x, 1/2+y, -z)

If they were correct, I'd still be missing three positions. These three positions are given by the binary axes. Here I have a serious problem because I don't know if this binary axis is normal ($$2$$) or helical ($$2_1$$).

After making these deductions, I check to see if I've done well:

After that, I realise that some of the equivalent positions do not coincide with those I have deduced. For example, the two of the sliding planes of type "n".

I also have mistakes that I can't explain or understand. These are the following:

a) Why is one of the binaries at 1/4? I've searched the Internet and I can't find any explanation that helps me much.

b) Why is the plane type "n" displaced? I would have placed it on the line of axis "b".

• I thought of adding a link to a very similar recent question... then I realized it was your question. What happened? Are you moving back in time? How can we help? – Ivan Neretin Aug 21 at 17:26
• Indeed, a month ago I asked that question and you answered it very cordially. The need for the question is that there are still aspects that I do not understand in the realization of these diagrams. It is not a time travel. – aprendiendo-a-programar Aug 21 at 17:38
• Well, my former answer applies to this problem just as well. How is it different, really? – Ivan Neretin Aug 21 at 18:00
• The problem is obviously similar. But, I went to solve it to the answer you gave me in your day and I didn't get the right diagram. The seven points you told me to follow are not very well understood and, therefore, I asked this new question. I hope that all of you can help me. @IvanNeretin – aprendiendo-a-programar Aug 22 at 8:53
• Go by the steps. Draw all the planes. Then deduce all axes and screw axes. Then the center. At each step compare your picture to the known result. Stop when you encounter the first differences. Where are we now? – Ivan Neretin Aug 22 at 8:57