Crystallographic space groups and group cohomology

I will start adding references on this topic here.

https://gap-packages.github.io/hap/tutorial/chap11_mj.html#X7C0B125E7D5415B4

A recent comment on GAP system:

https://github.com/gap-packages/hap/issues/69

GAP implementation of LHS spectral sequence:

https://gap-packages.github.io/hap/www/SideLinks/About/aboutSpaceGroup.html

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

https://math.stackexchange.com/questions/3146824/proof-that-there-exist-only-17-wallpaper-groups-tilings-of-the-plane

Then, an excellent outline of the proof by Michael Weiss (who is a distinguished professor in topology https://en.wikipedia.org/wiki/Michael_Weiss_(mathematician)):

https://diagonalargument.com/2020/04/26/wallpaper-groups/#more-1426

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, http://sierra.nmsu.edu/Morandi/notes/Wallpaper.pdf , is not working, but the following one is)

Mathematical Notes

https://drive.google.com/file/d/12fti6FKkwqlCyntRGAkXtjbrfUyw3p-g/view

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

https://arxiv.org/abs/cond-mat/0301601

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:

http://aflowlib.org/prototype-encyclopedia/enantiomorph_info.html

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