{
  "id": "1603.01710",
  "version": "v1",
  "published": "2016-03-05T11:04:24.000Z",
  "updated": "2016-03-05T11:04:24.000Z",
  "title": "Sporadic simple groups and locally toroidal polytopes",
  "authors": [
    "Dmitrii V. Pasechnik"
  ],
  "comment": "LaTeX, 7 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We construct new finite rank 6 locally toroidal regular polytopes of type {3,3,4,3,3}, disproving a long-standing conjecture of P.McMullen and E.Schulte. These (abstract) polytopes are related to a well-known Y-shaped presentation for the sporadic simple group $Fi_{22}$, and admit (covers of) $O_8^+(2){:}S_3$ as the automorphism group. We also discuss further extensions of these abstract polytopes, and pose a number of open questions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-05T11:04:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D08",
      "20D06",
      "51E24",
      "51F15",
      "52B70"
    ],
    "keywords": [
      "sporadic simple group",
      "locally toroidal polytopes",
      "locally toroidal regular polytopes",
      "well-known y-shaped presentation",
      "finite rank"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160301710P"
    }
  }
}