Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 1, pp. 267-273 (2004)

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Lattice packings with gap defects are not completely saturated

Greg Kuperberg, Krystyna Kuperberg and W{\l}odzimierz Kuperberg

Department of Mathematics, University of California, Davis, CA 95616 e-mail:; Department of Mathematics, Auburn University, Auburn, AL 36849, e-mail:; e-mail:

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 Tóth, 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 not completely saturated.

Keywords: circle packing, saturated packing, completely saturated packing

Classification (MSC2000): 52C15, 52C17

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Electronic version published on: 5 Mar 2004. This page was last modified: 4 May 2006.

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