Geodesic
On limits of dense packing of equal spheres in a cube
The electronic journal of combinatorics, Tome 22 (2015) no. 1
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We examine packing of $n$ congruent spheres in a cube when $n$ is close but less than the number of spheres in a regular cubic close-packed (ccp) arrangement of $\lceil p^{3}/2\rceil$ spheres. For this family of packings, the previous best-known arrangements were usually derived from a ccp by omission of a certain number of spheres without changing the initial structure. In this paper, we show that better arrangements exist for all $n\leq\lceil p^{3}/2\rceil-2$. We introduce an optimization method to reveal improvements of these packings, and present many new improvements for $n\leq4629$.
DOI : 10.37236/3784
Classification : 52C17, 05B40
Mots-clés : packing of \(n\) congruent spheres, cube 
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     author = {Milos Tatarevic},
     title = {On limits of dense packing of equal spheres in a cube},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {1},
     doi = {10.37236/3784},
     zbl = {1309.52008},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3784/}
}
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Milos Tatarevic. On limits of dense packing of equal spheres in a cube. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/3784

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