Simplest non-trivial closed knot with three crossings
This article is about the topological concept. For the protein fold, see
trefoil knot fold.
Trefoil |
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![](//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Blue_Trefoil_Knot_Animated.gif/220px-Blue_Trefoil_Knot_Animated.gif) |
Common name | Overhand knot |
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Arf invariant | 1 |
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Braid length | 3 |
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Braid no. | 2 |
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Bridge no. | 2 |
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Crosscap no. | 1 |
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Crossing no. | 3 |
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Genus | 1 |
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Hyperbolic volume | 0 |
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Stick no. | 6 |
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Tunnel no. | 1 |
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Unknotting no. | 1 |
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Conway notation | [3] |
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A–B notation | 31 |
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Dowker notation | 4, 6, 2 |
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Last / Next | 01 / 41 |
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alternating, torus, fibered, pretzel, prime, knot slice, reversible, tricolorable, twist |
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.
The trefoil knot is named after the three-leaf clover (or trefoil) plant.