7₄ knot

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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 74
Dowker notation 6, 10, 12, 14, 4, 2, 8
Last /Next 7375
alternating, hyperbolic, prime, reversible, tricolorable

In mathematical knot theory, 74 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.

Visual representations[edit]

One form of the Endless knot of Buddhism
Interwoven unicursal hexagram.

The image in the infobox at top right shows the 74 knot in Celtic artistic form, also found in some Hausa embroideries.[1]

The interlaced version of the simplest form of the Endless knot symbol of Buddhism is topologically equivalent to the 74 knot (though it appears to have nine crossings), as is the interlaced version of the unicursal hexagram of occultism.[2] (However, the endless knot symbol has more complex forms not equivalent to 74, and both the endless knot and unicursal hexagram can appear in non-interlaced versions, in which case they are not knots at all.)


  1. ^ Celtic Art: The Methods of Construction by George Bain, p. 27 (ISBN 0-486-22923-8)
  2. ^ "7_4", The Knot Atlas.