{
  "id": "1202.4701",
  "version": "v2",
  "published": "2012-02-21T17:01:35.000Z",
  "updated": "2013-05-06T16:22:14.000Z",
  "title": "The width of 5-dimensional prismatoids",
  "authors": [
    "Benjamin Matschke",
    "Francisco Santos",
    "Christophe Weibel"
  ],
  "comment": "31 pages, 10 figures. Changes from v1: the introduction has been edited, and a minor correction made in the statement of Proposition 1.5",
  "categories": [
    "math.CO"
  ],
  "abstract": "Santos' construction of counter-examples to the Hirsch Conjecture (2012) is based on the existence of prismatoids of dimension d of width greater than d. Santos, Stephen and Thomas (2012) have shown that this cannot occur in $d \\le 4$. Motivated by this we here study the width of 5-dimensional prismatoids, obtaining the following results: - There are 5-prismatoids of width six with only 25 vertices, versus the 48 vertices in Santos' original construction. This leads to non-Hirsch polytopes of dimension 20, rather than the original dimension 43. - There are 5-prismatoids with $n$ vertices and width $\\Omega(\\sqrt{n})$ for arbitrarily large $n$. Hence, the width of 5-prismatoids is unbounded.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-06T16:22:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B05",
      "52B55",
      "90C05"
    ],
    "keywords": [
      "prismatoids",
      "hirsch conjecture",
      "width greater",
      "original construction",
      "non-hirsch polytopes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.4701M"
    }
  }
}