7₁ knot | |
---|---|

Arf invariant | 0 |

Braid length | 7 |

Braid no. | 2 |

Bridge no. | 2 |

Crosscap no. | 1 |

Crossing no. | 7 |

Genus | 3 |

Hyperbolic volume | 0 |

Stick no. | 9 |

Unknotting no. | 3 |

Conway notation | [7] |

A-B notation | 7_{1} |

Dowker notation | 8, 10, 12, 14, 2, 4, 6 |

Last /Next | 6_{3} / 7_{2} |

Other | |

alternating, torus, fibered, prime, reversible |

In knot theory, the **7 _{1} knot**, also known as the

**septoil knot**, the

**septafoil knot**, or the

**(7, 2)-torus knot**, is one of seven prime knots with crossing number seven. It is the simplest torus knot after the trefoil and cinquefoil.

The 7_{1} knot is invertible but not amphichiral. Its Alexander polynomial is

its Conway polynomial is

and its Jones polynomial is

^{[1]}

## Example

## See also

## References

**^**"7_1",*The Knot Atlas*.