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he regular tetrahedron is the simplest Platonic solid. Nevertheless, in studying its packing properties, several renowned scholars have made mistakes, and many questions about it remain unsolved. Currently no one knows the density of its densest packings, the density of its densest translative packings, or the exact value of its congruent kissing number. In this paper we recount historical developments on packing regular tetrahedra, report new results on its translative packing density and congruent kissing number, and formulate several unsolved problems.
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Lagarias et al. (2012) studied this question.
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