{
  "id": "math/0310429",
  "version": "v2",
  "published": "2003-10-28T07:41:04.000Z",
  "updated": "2004-01-14T03:31:15.000Z",
  "title": "The Classification of Rank 4 Locally Projective Polytopes and Their Quotients",
  "authors": [
    "Michael I Hartley"
  ],
  "comment": "9 pages, 1 table",
  "categories": [
    "math.CO",
    "math.GT"
  ],
  "abstract": "This article announces the completion of the classification of rank 4 locally projective polytopes and their quotients. There are seventeen universal locally projective polytopes (nine nondegenerate). Amongst their 441 quotients are a further four (nonuniversal) regular polytopes, and 152 nonregular but section regular polytopes. All 156 of the latter have hemidodecahedral facets or hemi-icosahedral vertex figures. It is noted that, remarkably, every rank 4 locally projective section regular polytope is finite. The article gives a survey of the literature of locally projective polytopes and their quotients, and fills one small gap in the classification in rank 4.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-01-14T03:31:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51M20",
      "52B15"
    ],
    "keywords": [
      "universal locally projective polytopes",
      "classification",
      "locally projective section regular polytope",
      "hemi-icosahedral vertex figures",
      "hemidodecahedral facets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10429H"
    }
  }
}