An interesting part about operations for lattices rotations is presented in Kittel ch1. The small graph shows 6 operations where each one rotates the lattice by 2π/n, where n=1,2,3,4,5 or 6 for the six samples in the graph. All of them should be applied to a lattice point. For the operations 1 and 2 there are no restrictions on the rotation, unlike the rest. Operations 3 and 6 require a hexagonal lattice, but operation 4 requires a square one.
I thought the symmetry operations just rotation and reflection but i found they also include inversion and improper rotation. Also,I read that Rotation around a different axis is not necessarily a symmetry operation.
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