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

  • Author(s): Kuperberg, Greg
  • Kuperberg, Krystyna
  • Kuperberg, Wlodzimierz
  • et al.

Published Web Location

https://arxiv.org/pdf/math/0303366.pdf
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Abstract

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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