The densest lattice in twenty-four dimensions

Exact Constructions of a Family of Dense Periodic Packings of Tetrahedra

The determination of the densest packings of regular tetrahedra (one of the five Platonic solids) is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures that have emerged. Here we provide the most general analytical formulation to date to construct dense periodic packings of tetrahedra with four particles per fundamental cell. This analysis results in six-parameter family of dense tetrahedron packings that includes as special cases recently discovered "dimer" packings of tetrahedra, including the densest kno…

24维球堆积问题

The sphere packing problem in dimension 24

本文借鉴Viazovska八维球堆积问题的解法，证明24维空间中Leech格是最密且唯一的周期堆积，并构造了相应的最优辅助函数。