Geodesic
The Densest Packing of Six Spheres in a Cube
Canadian mathematical bulletin, Tome 9 (1966) no. 3, pp. 275-280

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This packing problem is obviously equivalent to the problem of locating six points Pi(l ≤ i ≤ 6) in a- closed unit cube C such that is as large as possible, where d(Pi, Pj) denotes the distance between Pi and Pj. 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 Ri(l≤i≤6) shown in fig. 1. Note that , and so the six points are the vertices of a regular octahedron. 
Schaer, J. The Densest Packing of Six Spheres in a Cube. Canadian mathematical bulletin, Tome 9 (1966) no. 3, pp. 275-280. doi: 10.4153/CMB-1966-035-5
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     title = {The {Densest} {Packing} of {Six} {Spheres} in a {Cube}},
     journal = {Canadian mathematical bulletin},
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     year = {1966},
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     number = {3},
     doi = {10.4153/CMB-1966-035-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-035-5/}
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