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arXiv · 1503.07933

On Limits of Dense Packing of Equal Spheres in a Cube

Milos Tatarevic
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Abstract

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 $n\leq4629$.

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Milos Tatarevic. 2015-03-27. On Limits of Dense Packing of Equal Spheres in a Cube. https://arxiv.org/abs/1503.07933

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