Crystallographic restriction theorem
= Crystallographic restriction theorem
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A rotation preserving a rank-two <lattice> has order $1,2,3,4$ or $6$. In a lattice basis its matrix is integral, while its trace is $2\cos\theta$. The only integral values in $[-2,2]$ are $-2,-1,0,1,2$, which give precisely those rotation orders. Finiteness of a symmetry group alone would not impose this restriction.