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arXiv · 1806.10878

New dense superball packings in three dimensions

Maria Dostert·Frank Vallentin
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Abstract

In this paper we construct a new family of lattice packings for superballs in three dimensions (unit balls for the $l^p_3$ norm) with $p \in (1, 1.58]$. We conjecture that the family also exists for $p \in (1.58, \log_2 3 = 1.5849625\ldots]$. Like in the densest lattice packing of regular octahedra, each superball in our family of lattice packings has $14$ neighbors.

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Maria Dostert, Frank Vallentin. 2018-06-28. New dense superball packings in three dimensions. https://doi.org/10.1515/advgeom-2020-0002

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