Kuperberg, Greg; Kuperberg, Krystyna; Kuperberg, Włodzimierz Lattice packings with gap defects are not completely saturated. (English) Zbl 1054.52010 Beitr. Algebra Geom. 45, No. 1, 267-273 (2004). A packing of unit spheres in \({\mathbb R}^n\) is \(k\)-saturated if it is not possible to replace \(k-1\) spheres by \(k\) spheres and still have a packing, and completely saturated if it is \(k\)-saturated for every \(k\).Considering the honeycomb packing in \({\mathbb R}^2\) and the fcc packing in \({\mathbb R}^3\) with linear (resp. planar) gap, the authors prove that rearrangement of finitely many circles (spheres) is possible to ensure enough space for a new circle (sphere). This means that such packings are not completely saturated. Some open questions in this area are listed. Reviewer: Peter Boyvalenkov (Sofia) Cited in 1 Document MSC: 52C15 Packing and covering in \(2\) dimensions (aspects of discrete geometry) 52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry) Keywords:honeycomb packing; fcc packing; saturated packings; circle packing PDFBibTeX XMLCite \textit{G. Kuperberg} et al., Beitr. Algebra Geom. 45, No. 1, 267--273 (2004; Zbl 1054.52010) Full Text: arXiv EuDML EMIS