Abstract
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 lattice packing D4 is the densest sphere packing in 4 dimensions.
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Dedicated to the 70th anniversary of Ted Bisztriczky, Gábor Fejes Tóth and Endre Makai
This research is partially supported by the NSF grant DMS1400876 and the RFBR grant 150199563.
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Musin, O.R. Towards a proof of the 24-cell conjecture. Acta Math. Hungar. 155, 184–199 (2018). https://doi.org/10.1007/s10474-018-0828-5
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DOI: https://doi.org/10.1007/s10474-018-0828-5