| 74 | |
| Arf Invariant: | 0 |
| Braid Length: | 9 |
| Braid Number: | 4 |
| Bridge Number: | 2 |
| Crosscap Number: | 3 |
| Crossing Number: | 7 |
| Genus: | 1 |
| Hyperbolic Volume: | 5.13794 |
| Stick Number: | 9 |
| Unknotting Number: | 2 |
| Conway Notation: | [313] |
| Ab Notation: | 74 |
| Dowker Notation: | 6, 10, 12, 14, 4, 2, 8 |
| Last Crossing: | 7 |
| Last Order: | 3 |
| Next Crossing: | 7 |
| Next Order: | 5 |
| Alternating: | alternating |
| Class: | hyperbolic |
| Prime: | prime |
| Symmetry: | reversible |
| Tricolorable: | 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.
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. (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[1]
\begin{aligned} x&=\cos(2t+0.22)\\ y&=\cos(3t+1.10)\\ z&=\cos7t \end{aligned}