Symmetry of Cyclohexane: How Many Vibrations in Its Spectrum?

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The discussion focuses on determining the point group of the chair conformer of cyclohexane, which is identified as D3h. The user calculates the expected number of vibrations, arriving at a total of 24, but believes it should be 18 based on starting with 18 vectors (3 for each carbon atom). The confusion arises from the application of equations related to vibrational modes. Participants are encouraged to identify where the miscalculation might have occurred. Clarifying the correct number of Raman and infrared active vibrations is essential for accurate spectral analysis.
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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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