Symmetry Operations and Classes

At this point, it is important to mention that, in spite of the great variety of active centers (molecules, ions in solids, color centers, etc.), it can be demonstrated that only 32 point symmetry groups exist in nature. These 32 point symmetry groups (denoted by the so-called Schoenflies symbols) are listed in Table 7.1. The group order and 

Symbol Group order Number of classes Crystalline system 

It can be seen that there are seven other symmetry operations (roto-reflections) of this class, which is then denoted by SSe, the subscript 6 indicating a rotation through lit 16. In a similar way, we can analyze other symmetry operations of classes 65 4,15 2 (commonly called an inversion symmetry operation and denoted by /), and IE (the identity operation that leaves the octahedron unchanged). 

In summary, the Oh group contains 48 symmetry operation elements belonging to the following ten different symmetry classes  

Fortunately, as we shall see in the next section, it is only necessary to work with classes rather than with symmetry operations, so that the problem is considerably simplified. 

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SYMMETRY OPERATIONS AND CLASSES 239 clockwise rotation produces the following changes in the ligand positions ... 

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