What's special about the point group 432?

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SUMMARY

The point group 432 is unique in that it is neither centrosymmetric nor piezoelectric, a distinction that sets it apart from all other non-centrosymmetric point groups. This phenomenon arises from the presence of both a 4-fold axis, which retains 7 nonzero piezoelectric coefficients, and a 3-fold axis, which nullifies these coefficients. The high symmetry of group 432 results in all characteristic vectors being zero. For a deeper understanding, refer to Nye's "Physical Properties of Crystals."

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  • Understanding of point group symmetry in crystallography
  • Familiarity with piezoelectricity concepts
  • Knowledge of tensor properties related to crystal structures
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Researchers in crystallography, materials scientists, and physicists interested in the properties of piezoelectric materials and point group symmetry.

johng23
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Every non-centrosymmetric point group is piezoelectric, except 432. It is neither centrosymmetric nor piezoelectric. Why?
 
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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.
 
well，as for 432, it has a much high symmetric, so all the vector of its charecterastics must be zero
 

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