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If matrix A represents a type I symmetry operation, we can calculate the rotation angle from the value of the A matrix trace. We must remember that the trace of A is invariant with respect to a base system transformation.
In a lattice base system the trace is an integer number, since the elements of the matrix are integers. In an orthonormal base system, the counter-clockwise rotation of an angle , for example, around the z axis is given by:
and then the trace is equal to .
We have then: an integer, from which it is seen that the values of compatible with a lattice base system are: 60,90, 120, 180, 240, 270,300, 360.
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