into an integer number of lattice vectors, so the entries of the rotation matrix in the lattice basis - and hence the trace - are necessarily integers. Similar as in other proofs, this implies that the only allowed rotational symmetries correspond to 1,2,3,4 or 6-fold invariance. For example, wallpapers and crystals cannot be rotated by 45° and remain invariant, the only possible angles are: 360°, 180°, 120°, 90° or 60°.

Example
*Consider a 60° (360°/6) rotation matrix with respect to the oblique lattice