7₄ knot

74
Arf invariant	0
Braid length	9
Braid no.	4
Bridge no.	2
Crosscap no.	3
Crossing no.	7
Hyperbolic volume	5.13794
Unknotting no.	2
Conway notation	[313]
A-B notation	74
Dowker notation	6, 10, 12, 14, 4, 2, 8
Last /Next	73 / 75
Other
alternating, hyperbolic, prime, reversible

One form of the Endless knot of Buddhism

Interwoven unicursal hexagram.

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 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.)

Wikimedia Commons has media related to 7 4 knots.

Sources

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