{
  "id": "1103.2051",
  "version": "v1",
  "published": "2011-03-10T14:48:23.000Z",
  "updated": "2011-03-10T14:48:23.000Z",
  "title": "Regular tessellations of the hyperbolic plane by fundamental domains of a Fuchsian group",
  "authors": [
    "Robert Yuncken"
  ],
  "comment": "4 pages",
  "journal": "Mosc. Math. J., 3 (2003), no. 1, 249-252",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "For positive integers p and q with 1/p + 1/q < 1/2, a tessellation of type {p,q} is a tessellation of the hyperbolic plane by regular p-gons with q p-gons meeting at each vertex. In this paper, a necessary and sufficient condition on the integers p and q is established to determine when a tessellation of type {p,q} can be realized as a tessellation of the hyperbolic plane by fundamental domains of some Fuchsian group. Specifically, a tessellation of type {p,q} is a tessellation by fundamental domains if and only if q has a prime divisor less than or equal to p.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-10T14:48:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20H10"
    ],
    "keywords": [
      "hyperbolic plane",
      "fundamental domains",
      "fuchsian group",
      "regular tessellations",
      "regular p-gons"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.2051Y"
    }
  }
}