# 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 knot, the trefoil is fundamental to the study of mathematical knot theory.

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 | 3_{1} |

Dowker notation | 4, 6, 2 |

Last /Next | 0_{1} / 4_{1} |

Other | |

alternating, torus, fibered, pretzel, prime, not slice, reversible, tricolorable, twist |

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