This review paper is devoted to the problems of sphere packings in 4 dimensions. The main goal is to find reasonable approaches for solutions to problems related to densest sphere packings in 4-dimensional Euclidean space. We consider two long-standing open problems: the uniqueness of maximum kissing arrangements in 4 dimensions and the 24-cell conjecture. Note that a proof of the 24-cell conjecture also proves that the checkerboard lattice packing D4 is the densest sphere packing in 4 dimensions.
Coincidences in 4 dimensions
The raspberries in three dimensions with at most two sizes of berry
Rotations in three, four, and five dimensions
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