{
  "id": "0805.3479",
  "version": "v1",
  "published": "2008-05-22T14:58:13.000Z",
  "updated": "2008-05-22T14:58:13.000Z",
  "title": "Locally Toroidal Polytopes and Modular Linear Groups",
  "authors": [
    "B. Monson",
    "Egon Schulte"
  ],
  "comment": "21 pages (to appear in Discrete Mathematics)",
  "categories": [
    "math.CO",
    "math.MG"
  ],
  "abstract": "When the standard representation of a crystallographic Coxeter group G (with string diagram) is reduced modulo the integer d>1, one obtains a finite group G^d which is often the automorphism group of an abstract regular polytope. Building on earlier work in the case that d is an odd prime, we here develop methods to handle composite moduli and completely describe the corresponding modular polytopes when G is of spherical or Euclidean type. Using a modular variant of the quotient criterion, we then describe the locally toroidal polytopes provided by our construction, most of which are new.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-22T14:58:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51M20",
      "20F55"
    ],
    "keywords": [
      "locally toroidal polytopes",
      "modular linear groups",
      "abstract regular polytope",
      "handle composite moduli",
      "crystallographic coxeter group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.3479M"
    }
  }
}