Three-twist knot | |
---|---|

Arf invariant | 0 |

Braid length | 6 |

Braid no. | 3 |

Bridge no. | 2 |

Crosscap no. | 2 |

Crossing no. | 5 |

Genus | 1 |

Hyperbolic volume | 2.82812 |

Stick no. | 8 |

Unknotting no. | 1 |

Conway notation | [32] |

A-B notation | 5_{2} |

Dowker notation | 4, 8, 10, 2, 6 |

Last /Next | 5_{1} / 6_{1} |

Other | |

alternating, hyperbolic, prime, reversible, twist |

In knot theory, the **three-twist knot** is the twist knot with three-half twists. It is listed as the **5 _{2} knot** in the Alexander-Briggs notation, and is one of two knots with crossing number five, the other being the cinquefoil knot.

The three-twist knot is a prime knot, and it is invertible but not amphichiral. Its Alexander polynomial is

its Conway polynomial is

and its Jones polynomial is

^{[1]}

Because the Alexander polynomial is not monic, the three-twist knot is not fibered.

The three-twist knot is a hyperbolic knot, with its complement having a volume of approximately 2.82812.

## Example

## References

**^**"5_2",*The Knot Atlas*.