List Of Prime Knots
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knot theory In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are ...
, prime knots are those knots that are indecomposable under the operation of
knot sum In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction plays a key role in the classifica ...
. The prime knots with ten or fewer crossings are listed here for quick comparison of their properties and varied naming schemes.


Table of prime knots


Six or fewer crossings


Seven crossings


Eight crossings


Nine crossings


Ten crossings


Higher

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Conway knot In mathematics, in particular in knot theory, the Conway knot (or Conway's knot) is a particular knot with 11 crossings, named after John Horton Conway. It is related by mutation to the Kinoshita–Terasaka knot, with which it shares the same ...
11n34 *
Kinoshita–Terasaka knot In knot theory, the Kinoshita–Terasaka knot is a particular prime knot. It has 11 crossings. The Kinoshita–Terasaka knot has a variety of interesting mathematical properties. It is related by mutation to the Conway knot, with which it shares ...
11n42


Table of prime links


Seven or fewer crossings


Higher


See also

* List of knots *
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 Prime knots *01 knot/Unknot - a simple un-knotted closed loop *31 knot/Trefoil knot - (2,3)-torus knot, the two lo ...
* Knot tabulation *
(−2,3,7) pretzel knot In geometric topology, a branch of mathematics, the (−2, 3, 7) pretzel knot, sometimes called the Fintushel–Stern knot (after Ron Fintushel and Ronald J. Stern), is an important example of a pretzel knot which exhibits various in ...


Notes


External links

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KnotInfo
, ''Indiana.edu''. {{DEFAULTSORT:Prime knots Knot theory Mathematics-related lists