crystallographic groups

[DanGrayson]

I wonder whether to write a chapter on crystallographic groups. Here are some references:

https://www.jstor.org/stable/2974820 https://www.amazon.com/X-ray-Crystallography-Gregory-S-Girolami/dp/1891389777 https://en.wikipedia.org/wiki/Space_group

[UlrikBuchholtz]

As a warm-up (and already a worthwhile result in itself), there's the classification of wallpaper groups.

Another intermediate result is the classification of the crystallographic point groups, or rather all point groups, which itself is a stepping-stone towards Klein's solution of the quintic via the symmetries of the icosahedron.