On rational directions in the flat lattice

Rational and irrational rotations for the set of rational directions in the flat point lattice are considered. It is proved that in the case of rational rotations an order of noncrystallographic turn can be only 8 or 12. The set of rational directions in the rectangular point lattice with metric quadratic form $x^2+\lambda^2y^2$ and arbitrary its centering has irrational rotation if and only if the number $\lambda^2$ is rational.
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