7_{4} | |
---|---|

Arf invariant | 0 |

Braid length | 9 |

Braid no. | 4 |

Bridge no. | 2 |

Crosscap no. | 3 |

Crossing no. | 7 |

Genus | 1 |

Hyperbolic volume | 5.13794 |

Stick no. | 9 |

Unknotting no. | 2 |

Conway notation | [313] |

A-B notation | 7_{4} |

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

Last /Next | 7<sub>3</sub> / 7<sub>5</sub> |

Other | |

alternating, hyperbolic, prime, reversible, tricolorable |

In mathematical knot theory, **7 _{4}** is the name of a 7-crossing knot which can be visually depicted in a highly-symmetric form, and so appears in the symbolism and/or artistic ornamentation of various cultures. This knot has 14 intersections with 7 crossing-over.

## Visual representations

The interlaced version of the simplest form of the Endless knot symbol of Buddhism is topologically equivalent to the 7_{4} knot (though it appears to have nine crossings), as is the interlaced version of the unicursal hexagram of occultism.^{[1]} (However, the endless knot symbol has more complex forms not equivalent to 7_{4}, and both the endless knot and unicursal hexagram can appear in non-interlaced versions, in which case they are not knots at all.)

Wikimedia Commons has media related to .7 4 knots |

## Example

## Sources

**^**"7_4",*The Knot Atlas*.**^***Celtic Art: The Methods of Construction*by George Bain, p. 27 (ISBN 0-486-22923-8)