A Density Bound for Efficient Packings of 3-space with Centrally Symmetric Convex Bodies

A New Packing Density Bound in 3-space

Abstract
It is shown that every compact convex set K which is centrally symmetric and has a non-empty interior admits a packing of Euclidean 3-space with density greater than or equal to 0.53835.... This is an improvement of the result in [9], which achieved a bound of 0.46421...Minkowski combinations and the Brunn-Minkowski inequality are used in conjunction with the construction in [9] to achieve a better result.