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.
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)