Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 35 (1994), No. 1, 67-71.

On Mixed Sphere Packings     

Salvatore Vassallo, J\"org M.\ Wills

Abstract. 

Balls of two different radii \ \hbox{$r_1<r_2$} \  can 
trivially be packed in $E^3$ with density better than the classical packing 
density \ \hbox{$\delta^3_L=0.74048\ldots{}$,} if \ \hbox{$r_1/r_2\le 0.41..$.} 
We show that this even holds for \ \hbox{$r_1/r_2=0.623\ldots{}$} Further we 
show, under strong restrictions, that $r_1/r_2$ close to 1 does not yield a 
density $>\delta^3_L$. 
These results correspond to similar results on circle packings in the 
plane by G. Blind, L. Fejes T\'oth and A. Florian.