{
  "id": "1501.06088",
  "version": "v1",
  "published": "2015-01-24T22:18:21.000Z",
  "updated": "2015-01-24T22:18:21.000Z",
  "title": "Geometry of lifts of tilings of euclidean spaces",
  "authors": [
    "Andrey Gavrilyuk"
  ],
  "comment": "23 pages, in Russian, accepted to \"Proceedings of the Steklov Institute of Mathematics\"",
  "categories": [
    "math.MG"
  ],
  "abstract": "This paper provides explicit justification for a method of canonical scalings of tilings of euclidean spaces. We present a new combinatorially-geometrical approach for constructing a generatriss of a tiling. The approach is based on an operation of lifting of a tile up to a lifted neighbour. We use this approach and give a new short geometrical proof of a fundamental theorem of theory of parallelotopes: Voronoi's Conjecture holds for a given parallelotope $P$ if and only if the corresponding tiling $\\mathcal T_P$ admits a canonical scaling.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-24T22:18:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "euclidean spaces",
      "voronois conjecture holds",
      "explicit justification",
      "short geometrical proof",
      "fundamental theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "ru",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150106088G"
    }
  }
}