{
  "id": "1712.04099",
  "version": "v1",
  "published": "2017-12-12T02:13:51.000Z",
  "updated": "2017-12-12T02:13:51.000Z",
  "title": "Towards a proof of the 24-cell conjecture",
  "authors": [
    "Oleg R. Musin"
  ],
  "comment": "18 pages",
  "categories": [
    "math.MG",
    "math.CO"
  ],
  "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 checkerboard lattice packing D4 is the densest sphere packing in 4 dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-12T02:13:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjecture",
      "densest sphere packing",
      "dimensions",
      "checkerboard lattice packing d4",
      "main goal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}