{
  "id": "1802.08947",
  "version": "v1",
  "published": "2018-02-25T03:06:02.000Z",
  "updated": "2018-02-25T03:06:02.000Z",
  "title": "$2$-groups behaving as automorphism groups of regular $3$-polytopes",
  "authors": [
    "Dong-Dong Hou",
    "Yan-Quan Feng",
    "Dimitri Leemans"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we classify regular polytopes with automorphism groups of order $2^n$ and Schl\\\"afli types $\\{4, 2^{n-3}\\}, \\{4, 2^{n-4}\\}$ and $\\{4, 2^{n-5}\\}$ for $n \\geq 10$, therefore giving a partial answer to a problem proposed by Schulte and Weiss in [Problems on polytopes, their groups, and realizations, Periodica Math. Hungarica 53(2006) 231-255].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-25T03:06:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B25",
      "20D15",
      "52B15"
    ],
    "keywords": [
      "automorphism groups",
      "groups behaving",
      "periodica math",
      "partial answer",
      "classify regular polytopes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}