Irreducible representations twofold degenerate

For the twofold degenerate irreducible representations, the following linear combinations are found ... 

In this table, there exist four non-degenerate Irreducible representations, one twofold degenerate and four fourfold degenerate. From this table and that of acetone with the cog-wheel effect, the equivalence relations between the irreducible representations of both groups are derivable. These are given in Table 13. 

Some of these symbols include degenerate irreducible representations. This means that two, three, or more vibrations are of the same energy and have the same frequency. For example twofold degeneracy can result when two vibrations are orthogonal, i.e. when their ampUtudes are at an angle of 90° to each other and of the same size. 

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