{
  "id": "math/9811074",
  "version": "v1",
  "published": "1998-11-11T06:26:42.000Z",
  "updated": "1998-11-11T06:26:42.000Z",
  "title": "Sphere packings II",
  "authors": [
    "Thomas C. Hales"
  ],
  "comment": "18 pages. Second of two older papers in the series on the proof of the Kepler conjecture. See math.MG/9811071. The original abstract is preserved",
  "journal": "Discrete Comput. Geom. 18 (1997), 135-149",
  "categories": [
    "math.MG"
  ],
  "abstract": "An earlier paper describes a program to prove the Kepler conjecture on sphere packings. This paper carries out the second step of that program. A sphere packing leads to a decomposition of $R^3$ into polyhedra. The polyhedra are divided into two classes. The first class of polyhedra, called quasi-regular tetrahedra, have density at most that of a regular tetrahedron. The polyhedra in the remaining class have density at most that of a regular octahedron (about 0.7209).",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-11-11T06:26:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sphere packing",
      "kepler conjecture",
      "second step",
      "earlier paper",
      "first class"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....11074H"
    }
  }
}