{
  "id": "math/0607447",
  "version": "v3",
  "published": "2006-07-19T02:35:49.000Z",
  "updated": "2008-09-09T01:40:56.000Z",
  "title": "The D_4 root system is not universally optimal",
  "authors": [
    "Henry Cohn",
    "John H. Conway",
    "Noam D. Elkies",
    "Abhinav Kumar"
  ],
  "comment": "11 pages, updated to incorporate small changes in published version",
  "journal": "Experimental Mathematics 16 (2007), 313-320",
  "doi": "10.1080/10586458.2007.10129008",
  "categories": [
    "math.MG"
  ],
  "abstract": "We prove that the D_4 root system (equivalently, the set of vertices of the regular 24-cell) is not a universally optimal spherical code. We further conjecture that there is no universally optimal spherical code of 24 points in S^3, based on numerical computations suggesting that every 5-design consisting of 24 points in S^3 is in a 3-parameter family (which we describe explicitly, based on a construction due to Sali) of deformations of the D_4 root system.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-09-09T01:40:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "root system",
      "universally optimal spherical code",
      "conjecture",
      "numerical computations",
      "construction"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7447C"
    }
  }
}