{
  "id": "1602.02987",
  "version": "v1",
  "published": "2016-02-09T14:05:38.000Z",
  "updated": "2016-02-09T14:05:38.000Z",
  "title": "Any Finite Group is the Group of Some Binary, Convex Polytope",
  "authors": [
    "Jean-Paul Doignon"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For any given finite group, Schulte and Williams (2015) produce a convex polytope whose combinatorial automorphisms form a group isomorphic to the given group. We provide here a shorter proof for a stronger result: the convex polytope we build for the given finite group is binary, and even combinatorial in the sense of Naddef and Pulleyblank (1981); the diameter of its skeleton is at most 2; any automorphism of the skeleton is a combinatorial automorphism; any combinatorial automorphism of the polytope is induced by some isometry of the space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-09T14:05:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E18",
      "52B15"
    ],
    "keywords": [
      "finite group",
      "convex polytope",
      "combinatorial automorphisms form",
      "group isomorphic",
      "shorter proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160202987D"
    }
  }
}