Symmetry of Cyclohexane: How Many Vibrations in Its Spectrum?

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Homework Statement


Determine the point group of the chair conformer of cyclohexane. How many Raman active vibrations and how many infrared active vibrations might you expect to detect in its spectrum?


Homework Equations



(see link below)

The Attempt at a Solution



http://img442.imageshack.us/img442/240/symmetrycw.jpg

Im rubbish with LaTex so I've hosted a picture of what I've done in word. I've determined the point group to be D3h but when I use the equation to get the values for the different vibrations, I get a total of 24 when it should be 18 because I started with 18 vectors (3 on each carbon). I am not sure where I am going wrong. Thanks.
 
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