An alternative proof consider matrix properties is harder for higher dimensions, using this diagram. The general crystallographic restriction does guarantee not that a rotation. Example work not with a square lattice, has an eightfold rotational symmetry. This view be described from a 4D lattice as the projection of a slab cut. This third matrix corresponds then by 45 ° to a rotation. Rotational symmetry of any order is compatible along that axis with translational symmetry.