As I'm interested in the simplifications of property tensors due to crystal symmetry, I have been trying to find the symmetries of silicon (i.e. the diamond structure). As silicon belongs to the m3m point group I would e.g. expect to find a mirror plane perpendicular to the ,  and  directions. I have, however, not been able to locate the coordinate system in which these (and all the other m3m symmetries) exists. The standard cubic crystal axes do as far as I can see not include these symmetries. Do anybody know which coordinate system one should use in order to obtain all symmetries of the m3m point group?