Bezdek, Károly Compact packings in the Euclidean space. (English) Zbl 0619.52010 Beitr. Algebra Geom. 25, 79-84 (1987). A packing of convex bodies in \({\mathbb{E}}^ n\) is said to be compact if any continuous curve which connects an arbitrary body of the packing with a point sufficiently distant from the body, intersects at least one body of the packing touching the body under consideration. L. Fejes Tóth (oral communication) proved that the lower density of a compact packing of homothetic centrally symmetric convex discs with ratios of diameters bounded is at least 3/4. If the central symmetry is dropped then the lower density is at least 1/2 as shown by A. Bezdek, the author and K. Böröczky [Stud. Sci. Math. Hung., to appear]. The author shows that the density of a compact lattice packing of a centrally symmetric convex body in \({\mathbb{E}}^ n\) is greater than \(2^{1/(n-1)}/(2^{1/(n-1)}+1).\) Reviewer: P.Gruber Cited in 1 Document MSC: 52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry) 52A40 Inequalities and extremum problems involving convexity in convex geometry Keywords:chess-board; density; compact lattice packing; centrally symmetric convex body PDFBibTeX XMLCite \textit{K. Bezdek}, Beitr. Algebra Geom. 25, 79--84 (1987; Zbl 0619.52010) Full Text: EuDML