  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.
