Building the Symmetry Groups

In the previous section it had been exposed how the symmetry elements of a structure generate associated operations. 

The relation number — symmetry is obviously at the levels of the rotations axes, but less clear in relation with the other operations and even lesser immediate when it comes to be global characterized, through a unique number, all the symmetry operations allowed by a structure. 

TABLE 2.1 The Symmetry Elements and Operations Associated Types (Putz, 2006) 

Inversion center I The inversion transformation (identical with the operation S. In Cartesian systems generates the coordinates inversion (x,y,z) - [-x,-y,-z). 

Proper axis of rotation C n The rotation (positive in clockwise sense) with the angle of In In radians, with n natural number. The axis of the biggest n is called the main rotation axis. 

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