Group Cohomology and Quasicrystals II: The Three Crystallographic Invariants in Two and Three Dimensions

BENJI N. FISHER, DAVID A. RABSON
2004 Ferroelectrics (Print)  
In Fourier-space crystallography, space groups are classified by their phase functions, Φ, and we can determine Φ (up to a gauge) by its invariants. Usually, the invariants imply necessary extinctions in diffraction, but among the 157 periodic non-symmorphic space groups, two are distinguished not by extinctions-they have none-but by a second type of invariant. We give a non-periodic example of a third type of invariant and assert that all invariants can be expressed as sums of just these three types.
doi:10.1080/00150190490462298 fatcat:duyuwhn5dzhnjdj4uei6673nom