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A new theory by Abhiram Reddy, Greg Grason et al., was recently published in PNAS

Formation of Frank–Kasper phases in soft matter systems confounds intuitive notions that equilibrium states achieve maximal symmetry, deriving from the conflict between symmetry of spherical domains and uniform space filling.  A new theory by Abhiram Reddy, Michael Buckley, Greg Grason and collaborators at University of Minnesota, published in the Proceedings of the National Academy of Sciences, shows how the structure and thermodynamics of complex sphere phases can be understood through a connection to two classic problems in cellular geometry: the Kelvin and Quantizer problems.

PNAS.org

October 15, 2018