The Densest Packing of Six Spheres in a Cube

Abstract

This packing problem is obviously equivalent to the problem of locating six points P i (l ≤ i ≤ 6) in a- closed unit cube C such that is as large as possible, where d(P i , P j ) denotes the distance between P i and P j . We shall prove that 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 i (l≤i≤6) shown in fig. 1. Note that , and so the six points are the vertices of a regular octahedron.