World Library  
Flag as Inappropriate
Email this Article

List of mathematical knots and links

Article Id: WHEBN0001168363
Reproduction Date:

Title: List of mathematical knots and links  
Author: World Heritage Encyclopedia
Language: English
Subject: Unknot, Perko pair, 7₁ knot, 6₃ knot, 6₂ knot
Collection: Knot Theory, Mathematics-Related Lists
Publisher: World Heritage Encyclopedia

List of mathematical knots and links

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


  • Knots 1
    • Prime knots 1.1
    • Composite 1.2
  • Links 2
  • External links 3


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

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.