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arXiv · 1506.04171

Regular Totally Separable Sphere Packings

Samuel Reid
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Abstract

The topic of totally separable sphere packings is surveyed with a focus on regular constructions, uniform tilings, and contact number problems. An enumeration of all regular totally separable sphere packings in $\mathbb{R}^2$, $\mathbb{R}^3$, and $\mathbb{R}^4$ which are based on convex uniform tessellations, honeycombs, and tetracombs, respectively, is presented, as well as a construction of a family of regular totally separable sphere packings in $\mathbb{R}^d$ that is not based on a convex uniform $d$-honeycomb for $d \geq 3$.

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Samuel Reid. 2015-06-06. Regular Totally Separable Sphere Packings. https://arxiv.org/abs/1506.04171

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