Exceptional properties of some sphere packings in the general position of P6222
Three types of sphere packing are described which show properties that have never been observed before: a certain set of generating symmetry operations corresponds to a parameter range in P6222 that is not simply connected, but disintegrates into two disjoint non-congruent regions; the minimal sphere-packing density is different for these two regions; two sphere packings from different regions cannot be deformed into each other without opening sphere contacts although their sphere-packing graphs are isomorphic in the graph-theoretical sense. Two heterogeneous crystal nets with different symmetry described by Delgado-Friedrichs & O'Keeffe [Acta Cryst. (2003), A59, 351–360] show a similar behaviour. They are related to a type of tetragonal sphere packing with likewise unusual properties.
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