{
  "id": "1110.1715",
  "version": "v1",
  "published": "2011-10-08T09:42:09.000Z",
  "updated": "2011-10-08T09:42:09.000Z",
  "title": "Determining All Universal Tilers",
  "authors": [
    "David G. L. Wang"
  ],
  "comment": "18 pages, 12 figures",
  "doi": "10.1007/s00454-012-9445-1",
  "categories": [
    "math.MG",
    "math.CO"
  ],
  "abstract": "A universal tiler is a convex polyhedron whose every cross-section tiles the plane. In this paper, we introduce a certain slight-rotating operation for cross-sections of pentahedra. Based on a selected initial cross-section and by applying the slight-rotating operation suitably, we prove that a convex polyhedron is a universal tiler if and only if it is a tetrahedron or a triangular prism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-08T09:42:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B45",
      "52C20"
    ],
    "keywords": [
      "universal tiler",
      "convex polyhedron",
      "slight-rotating operation",
      "cross-section tiles",
      "determining"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.1715W"
    }
  }
}