Lattice packings with gap defects are not completely saturated

Details Lattice packings with gap defects are not completely saturated Lattice packings with gap defects are not completely saturated

2003-03-28

arxiv.org/abs/math/0303366v1

Mathematics

Metric Geometry

Scientific paper

We show that a honeycomb circle packing in $\R^2$ with a linear gap defect cannot be completely saturated, no matter how narrow the gap is. The result is motivated by an open problem of G. Fejes T\'oth, G. Kuperberg, and W. Kuperberg, which asks whether of a honeycomb circle packing with a linear shift defect is completely saturated. We also show that an fcc sphere packing in $\R^3$ with a planar gap defect is also not completely saturated.

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