What's special about the point group 432?

[johng23]

Every non-centrosymmetric point group is piezoelectric, except 432. It is neither centrosymmetric nor piezoelectric. Why?

 

[johng23]

Well I guess there isn't really an intuitive reason for this, you just have to do the calculation. If anyone is interested, you can look in Nye's "Physical Properties of Crystals". It turns out that the 4-fold axis leaves 7 of the piezoelectric coefficients nonzero, and the 3 fold axis destroys all of these. 432 is the only group with both a 4 fold and a 3 fold axis.

 

[luoye]

well，as for 432, it has a much high symmetric, so all the vector of its charecterastics must be zero