I'm interested in the mathematics of crystals and quasicrystals--things like the enumeration of Bravais lattices and space groups, Bieberbach's results on higher dimensional lattices, and the cut and project construction for quasicrystals. Could someone suggest a reference for this?
Also, from the Wikipedia article on space groups, it looks like the enumeration of these groups is a complicated ad hoc procedure which tripped up pretty much everyone who attempted a solution. If anyone could comment on systematic or algorithmic approaches to this problem, I would appreciate it.
The book On Quaternions and Octonions has a systematic enumeration of the 3 and 4 dimensional groups in Chapters 3 and 4.