DNA and the double helix: statistical equilibrium and Neumann's   principle
  Neumann's principle (that the symmetry of a crystal measurement cannot be lower than that of its point-group) is a corner- stone of crystallography: were it false, then the technique of x-ray diffraction (double-helix, DNA) might well not exist. The literature variously regards its truth as obvious, intuitive, axiomatic or even impossible [10], without further analysis or proof. After identifying and correcting a false lead/start, we give a plausible proof of Neumann's principle, using group theory and quantum statistical mechanics. 
Michael J. Caola