{
  "id": "math/0302056",
  "version": "v2",
  "published": "2003-02-05T21:43:48.000Z",
  "updated": "2018-07-09T19:22:39.000Z",
  "title": "Uniqueness and Symmetry in Problems of Optimally Dense Packings",
  "authors": [
    "Lewis Bowen",
    "Charles Holton",
    "Charles Radin",
    "Lorenzo Sadun"
  ],
  "comment": "Updated 2018 to version published in 2005. Plain TeX, 27 pages of text followed by 11 figures",
  "journal": "Math Phys. Electron. J. 11 (2005) paper 1",
  "categories": [
    "math.MG",
    "math.DS"
  ],
  "abstract": "We analyze the general problem of determining optimally dense packings, in a Euclidean or hyperbolic space, of congruent copies of some fixed finite set of bodies. We are strongly guided by examples of aperiodic tilings in Euclidean space and a detailed analysis of a new family of examples in the hyperbolic plane. Our goal is to understand qualitative features of such optimum density problems, in particular the appropriate meaning of the uniqueness of solutions, and the role of symmetry in classfying optimally dense packings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-02-05T21:43:48.000Z",
      "comment": "Plain TeX, 27 pages of text followed by 11 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2018-07-09T19:22:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A40",
      "52C26",
      "52C23"
    ],
    "keywords": [
      "uniqueness",
      "optimum density problems",
      "general problem",
      "determining optimally dense packings",
      "hyperbolic space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......2056B"
    }
  }
}