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 the two loose ends of a common overhand knot, resulting in a knotted loop. As the simplest knot, the trefoil is fundamental to the study of mathematical knot theory.

This article is about the topological concept. For the protein fold, see trefoil knot fold.
Trefoil
Common nameOverhand knot
Arf invariant1
Braid length3
Braid no.2
Bridge no.2
Crosscap no.1
Crossing no.3
Genus1
Hyperbolic volume0
Stick no.6
Tunnel no.1
Unknotting no.1
Conway notation[3]
A–B notation31
Dowker notation4, 6, 2
Last / Next01 / 41
Other
alternating, torus, fibered, pretzel, prime, knot slice, reversible, tricolorable, twist

The trefoil knot is named after the three-leaf clover (or trefoil) plant.

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