{
  "id": "1808.06276",
  "version": "v1",
  "published": "2018-08-20T00:32:21.000Z",
  "updated": "2018-08-20T00:32:21.000Z",
  "title": "On the knot quandle of the twist-spun trefoil",
  "authors": [
    "Ayumu Inoue"
  ],
  "comment": "11 pages, 4 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that the knot quandle of the $3$-, $4$-, or $5$-twist-spun trefoil is isomorphic to a quandle related to the $16$-, $24$-, or $600$-cell respectively. We further show that the cardinality of the knot quandle of the $m$-twist-spun trefoil is finite if and only if $1 \\leq m \\leq 5$. This phenomenon is attributable to the fact that the regular tessellation $\\{ 3, m \\}$, in the sense of the Schl\\\"{a}fli symbol, consists of infinite triangles if $m$ is greater than or equal to 6.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-20T00:32:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q45",
      "52B15"
    ],
    "keywords": [
      "twist-spun trefoil",
      "knot quandle",
      "regular tessellation",
      "infinite triangles",
      "cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}