Simplest non-trivial closed knot with three crossings
This article is about the topological concept. For the protein fold, see
trefoil knot fold.
| Trefoil |
|---|
 |
| Common name | Overhand knot |
|---|
| Arf invariant | 1 |
|---|
| Braid length | 3 |
|---|
| Braid no. | 2 |
|---|
| Bridge no. | 2 |
|---|
| Crosscap no. | 1 |
|---|
| Crossing no. | 3 |
|---|
| Genus | 1 |
|---|
| Hyperbolic volume | 0 |
|---|
| Stick no. | 6 |
|---|
| Tunnel no. | 1 |
|---|
| Unknotting no. | 1 |
|---|
| Conway notation | [3] |
|---|
| A–B notation | 31 |
|---|
| Dowker notation | 4, 6, 2 |
|---|
| Last / Next | 01 / 41 |
|---|
|
| 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.
