symmetry of cyclohexane

unknownuser9

1. The problem statement, all variables and given/known data
Determine the point group of the chair conformer of cyclohexane. How many Raman active vibrations and how many infra-red active vibrations might you expect to detect in its spectrum?


2. Relevant equations

(see link below)

3. The attempt at a solution

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

Im rubbish with LaTex so ive hosted a picture of what ive done in word. Ive 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). Im not sure where im going wrong. Thanks.

unknownuser9

Any ideas?