A New Packing Density Bound in 3-Space

It is shown that every compact convex set K which is centrally symmetric and has a non-empty interior admits a lattice packing of Euclidean 3-space with density greater than or equal to 0.53835.... This is an improvement of the result in [8], which achieved a bound of 0.46421.... Minkowski combinations and the Brunn-Minkowski inequality are used in conjunction with the construction in [8] to achieve a better result.

Authors and Affiliations

1. MCIS Department, Jacksonville State University, Jacksonville, AL 36265 , USA

   Edwin H. Smith

Corresponding author

Correspondence to Edwin H. Smith.

Reprints and permissions