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

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 0.46421.... The best such bound previously known is 0.30051... due to the theorem of Minkowski-Hlawka. It is probable that there is such a lower bound which is significantly greater than the one shown in this note, since there is a packing of congruent spheres which has a density of pi/sqrt(18) = 0.74048....