7₄ knot

74
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	7<sub>3</sub> / 7<sub>5</sub>
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.

Visual representations

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.)

The 7₄ knot is a Lissajous knot, representable for example by the parametric equation^[2]

${\displaystyle {\begin{aligned}x&=\cos(2t+0.22)\\y&=\cos(3t+1.10)\\z&=\cos 7t\end{aligned}}}$

• 
  One form of the Endless knot of Buddhism
• 
  Interwoven unicursal hexagram.
• 
  7₄ knot in Celtic artistic form, also found in some Hausa embroideries.^[3]
• 
  A 7₄ knot combined with the Syrian flag is used as a logo by the National Coordination Committee for Democratic Change.

Wikimedia Commons has media related to 7 4 knots.

Example

Sources

This page was last edited on 10 March 2024, at 16:33