{
  "id": "math/0304492",
  "version": "v2",
  "published": "2003-04-30T13:54:28.000Z",
  "updated": "2004-03-17T14:45:53.000Z",
  "title": "The $E_t$-Construction for Lattices, Spheres and Polytopes",
  "authors": [
    "Andreas Paffenholz",
    "Günter M. Ziegler"
  ],
  "comment": "21 pages, many figures",
  "categories": [
    "math.MG",
    "math.CO"
  ],
  "abstract": "We describe and analyze a new construction that produces new Eulerian lattices from old ones. It specializes to a construction that produces new strongly regular cellular spheres (whose face lattices are Eulerian). The construction does not always specialize to convex polytopes; however, in a number of cases where we can realize it, it produces interesting classes of polytopes. Thus we produce an infinite family of rational 2-simplicial 2-simple 4-polytopes, as requested by Eppstein, Kuperberg and Ziegler. We also construct for each $d\\ge3$ an infinite family of $(d-2)$-simplicial 2-simple $d$-polytopes, thus solving a problem of Gr\\\"unbaum.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-03-17T14:45:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B11",
      "06A07"
    ],
    "keywords": [
      "construction",
      "strongly regular cellular spheres",
      "face lattices",
      "infinite family",
      "produces interesting classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......4492P"
    }
  }
}