This article contains a list of mathematical knots and links. See also

list of knots This list of knots includes many alternative names for common knots and lashings. Knot names have evolved over time, and there are many conflicting or confusing naming issues. The overhand knot, for example, is also known as the thumb knot. The ...

list of geometric topology topics This is a list of geometric topology topics, by Wikipedia page. See also: *topology glossary *List of topology topics *List of general topology topics *List of algebraic topology topics * Publications in topology Low-dimensional topology Knot the ...

Knots

Prime knots

*0₁ knot/

Unknot In the mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without a knot tied into it, unknotted. To a knot theorist, an unknot is any embe ...

- a simple un-knotted closed loop *3₁ knot/

Trefoil knot In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining together the two loose ends of a common overhand knot, resulting in a knotted loop. As the simplest ...

- (2,3)-torus knot, the two loose ends of a common overhand knot joined together *4₁ knot/

Figure-eight knot (mathematics) Figure 8 (figure of 8 in British English) may refer to: * 8 (number), in Arabic numerals Entertainment * ''Figure 8'' (album), a 2000 album by Elliott Smith * "Figure of Eight" (song), a 1989 song by Paul McCartney * ''Figure Eight EP'', a ...

- 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 star polygon (

pentagram A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon. Drawing a circle arou ...

) *5₂ knot/ Three-twist knot - the twist knot with three-half twists *6₁ knot/

Stevedore knot (mathematics) In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 62 knot and the 63 knot. The stevedore knot is listed as the 61 knot in the Alexander–Briggs notation, and it can also be descri ...

- 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 star polygon (

heptagram A heptagram, septagram, septegram or septogram is a seven-point star drawn with seven straight strokes. The name ''heptagram'' combines a numeral prefix, ''hepta-'', with the Greek suffix ''-gram''. The ''-gram'' suffix derives from ''γρ� ...

) * 7₄ knot, "endless knot" * 8₁₈ knot, "carrick mat" *10₁₆₁/10₁₆₂, known as the

Perko pair In the mathematical theory of knots, the Perko pair, named after Kenneth Perko, is a pair of entries in classical knot tables that actually represent the same knot. In Dale Rolfsen's knot table, this supposed pair of distinct knots is labeled 10 ...

; this was a single knot listed twice in Dale Rolfsen's knot table; the duplication was discovered by Kenneth Perko *12n242/

(−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 ...

*(''p'', ''q'')-

torus knot In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies on the surface of a torus in the same way. Each torus knot is specified by a pair of cop ...

- a special kind of knot that lies on the surface of an unknotted torus in R³

Composite

Square knot (mathematics) In knot theory, the square knot is a composite knot obtained by taking the connected sum of a trefoil knot with its reflection. It is closely related to the granny knot, which is also a connected sum of two trefoils. Because the trefoil kno ...

- a composite knot obtained by taking the connected sum of a trefoil knot with its reflection *

Granny knot (mathematics) In knot theory, the granny knot is a composite knot obtained by taking the connected sum of two identical trefoil knots. It is closely related to the square knot, which can also be described as a connected sum of two trefoils. Because the tr ...

- a composite knot obtained by taking the connected sum of two identical trefoil knots

Links

*0 link/

Unlink In the mathematics, mathematical field of knot theory, an unlink is a Link (knot theory), link that is equivalent (under ambient isotopy) to finitely many disjoint circles in the plane. Properties * An ''n''-component link ''L'' ⊂&nbs ...

- equivalent under ambient isotopy to finitely many disjoint circles in the plane *2 link/

Hopf link In mathematical knot theory, the Hopf link is the simplest nontrivial link with more than one component. It consists of two circles linked together exactly once, and is named after Heinz Hopf. Geometric realization A concrete model consists o ...

- the simplest nontrivial link with more than one component; it consists of two circles linked together exactly once (L2a1) *4 link/ Solomon's knot (a two component "link" rather than a one component "knot") - a traditional decorative motif used since ancient times (L4a1) *5 link/

Whitehead link In knot theory, the Whitehead link, named for J. H. C. Whitehead, is one of the most basic links. It can be drawn as an alternating link with five crossings, from the overlay of a circle and a figure-eight shaped loop. Structure A common w ...

- 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) *

Brunnian link In knot theory, a branch of topology, a Brunnian link is a nontrivial link that becomes a set of trivial unlinked circles if any one component is removed. In other words, cutting any loop frees all the other loops (so that no two loops can be ...

- a nontrivial link that becomes trivial if any component is removed *6 link/

Borromean rings In mathematics, the Borromean rings are three simple closed curves in three-dimensional space that are topologically linked and cannot be separated from each other, but that break apart into two unknotted and unlinked loops when any one of the t ...

- three topological circles which are linked and form a Brunnian link (L6a4) * L10a140 link - presumably the simplest non-Borromean Brunnian link *

Pretzel link In the mathematical theory of knots, a pretzel link is a special kind of link. It consists of a finite number tangles made of two intertwined circular helices. The tangles are connected cyclicly, the first component of the first tangle is con ...

- a Montesinos link with integer tangles

External links

* {{Knot theory Knots and links Knot theory