Crystallographic space groups and group cohomology

I will start adding references on this topic here.

A recent comment on GAP system:

GAP implementation of LHS spectral sequence:

Case of 2D: 17 wallpaper groups, 13 arithmetic classes. There are many materials talking about them. First, a nice summary:

Then, an excellent outline of the proof by Michael Weiss (who is a distinguished professor in topology

Click to access wallpaper-notes.pdf

And this note brings to the ultimate material that I was looking for — a book by Patrick Morandi (the original source, , is not working, but the following one is)

Mathematical Notes

The paper “Cohomology for Anyone” by David A. Rabson, John F. Huesman,and Benji N. Fisher:

Several papers by Michel;

The book N-dimensional crystallography by R. L. E. Schwarzenberger

219 Space groups becomes 230 Space groups when resolving chirality (enantiomorphic).

The eleven enantiomorphic groups are listed here:

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