List of mathematical knots and links

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This article contains a list of mathematical knots and links. See also list of knots, list of geometric topology topics.


Prime knots

  • 0₁ knot/Unknot - a simple un-knotted closed loop
  • 3₁ knot/Trefoil knot - (2,3)-torus knot, the two loose ends of a common overhand knot joined together
  • 4₁ knot/Figure-eight knot (mathematics) - a prime knot with a crossing number four
  • 5₁ knot/Cinquefoil knot, (5,2)-torus knot, Solomon's seal knot, pentafoil knot - a prime knot with crossing number five which can be arranged as a pentagram
  • 5₂ knot/Three-twist knot - the twist knot with three-half twists
  • 6₁ knot/Stevedore knot (mathematics) - a prime knot with crossing number six, it can also be described as a twist knot with four twists
  • 6₂ knot - a prime knot with crossing number six
  • 6₃ knot - a prime knot with crossing number six
  • 7₁ knot, septafoil knot, (7,2)-torus knot - a prime knot with crossing number seven, which can be arranged as a {7,2} star polygon
  • 7₄ knot, "endless knot"
  • 818 knot, "carrick mat"
  • 10₁₆₁/Perko pair
  • 12n242/(−2,3,7) pretzel knot
  • (pq)-torus knot - a special kind of knot that lies on the surface of an unknotted torus in R3



  • 02
    link/Unlink - equivalent under ambient isotopy to finitely many disjoint circles in the plane
  • 22
    link/Hopf link - the simplest nontrivial link with more than one component; it consists of two circles linked together exactly once (L2a1)
  • 42
    link/Solomon's knot (a two component "link" rather than a one component "knot") - a traditional decorative motif used since ancient times (L4a1)
  • 52
    link/Whitehead link - two projections of the unknot: one circular loop and one figure eight-shaped loop intertwined such that they are inseparable and neither loses its form (L5a1)
  • 63
    link/Borromean rings - three topological circles which are linked and form a Brunnian link (L6a4)
  • L10a140 link - presumably the simplest non-Borromean Brunnian link
  • Brunnian link - a nontrivial link that becomes trivial if any component is removed
  • Pretzel link - a Montesinos link with integer tangles

External links