{
  "id": "1409.6701",
  "version": "v1",
  "published": "2014-09-23T19:13:46.000Z",
  "updated": "2014-09-23T19:13:46.000Z",
  "title": "Lattice 3-polytopes with five lattice points",
  "authors": [
    "Mónica Blanco",
    "Francisco Santos"
  ],
  "comment": "19 pages, 11 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We work out the complete classification of lattice $3$-polytopes with exactly $5$ lattice points. We first show that for each $n$ there is only a finite number of (equivalence classes of) $3$-polytopes of lattice width larger than one. Since polytopes of width one are easy to classify, we concentrate on an exhaustive classification of those of width larger than one. For $n=4$, all empty tetrahedra have width one (White). For $n=5$ we show that there are exactly 9 different polytopes of width $2$, and none of larger width. Eight of them are the clean tetrahedra previously classified by Kasprzyk and (independently) Reznick.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-23T19:13:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B10",
      "52B20"
    ],
    "keywords": [
      "lattice points",
      "lattice width larger",
      "empty tetrahedra",
      "finite number",
      "clean tetrahedra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.6701B"
    }
  }
}