6₂ knot | |
---|---|

Arf invariant | 1 |

Braid length | 6 |

Braid no. | 3 |

Bridge no. | 2 |

Crosscap no. | 2 |

Crossing no. | 6 |

Genus | 2 |

Hyperbolic volume | 4.40083 |

Stick no. | 8 |

Unknotting no. | 1 |

Conway notation | [312] |

A-B notation | 6_{2} |

Dowker notation | 4, 8, 10, 12, 2, 6 |

Last /Next | 6_{1} / 6_{3} |

Other | |

alternating, hyperbolic, fibered, prime, reversible, twist |

In knot theory, the **6 _{2} knot** is one of three prime knots with crossing number six, the others being the stevedore knot and the 6

_{3}knot. This knot is sometimes referred to as the

**Miller Institute knot**,

^{[1]}because it appears in the logo

^{[2]}of the Miller Institute for Basic Research in Science at the University of California, Berkeley.

The 6_{2} knot is invertible but not amphichiral. Its Alexander polynomial is

its Conway polynomial is

and its Jones polynomial is

^{[3]}

The 6_{2} knot is a hyperbolic knot, with its complement having a volume of approximately 4.40083.

## Surface

## Example

Ways to assemble of knot 6.2