The densest packing of six spheres in a cube

J. Schaer
1966 Canadian mathematical bulletin  
This packing problem is obviously equivalent to the problem of locating six points P.(l<.i<.6) in a-closed unit cube C such that min d(P.,P.) is as large as possible, where d(P.,P.) denotes the distance between P. and P. . We shall prove that i J this minimum distance cannot exceed --(=m, say), and that 4 it attains this value only if the points form a configuration which is congruent to the one of the points R.(l<i<6) shown in fig. 1 .
doi:10.4153/cmb-1966-035-5 fatcat:wdy6wqsdkvf4fktchp35k6nrbu