7₄ knot

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74
Blue 7 4 Knot.png
Arf invariant0
Braid length9
Braid no.4
Bridge no.2
Crosscap no.3
Crossing no.7
Genus1
Hyperbolic volume5.13794
Stick no.9
Unknotting no.2
Conway notation[313]
A-B notation74
Dowker notation6, 10, 12, 14, 4, 2, 8
Last /Next7375
Other
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. This knot has 14 intersections with 7 crossing-over.

Visual representations[edit]

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.[1] (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.)

Example[edit]

Assembling of 7₄ knot.

Sources[edit]

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