| 62 knot | |
| Arf Invariant: | 1 |
| Braid Length: | 6 |
| Braid Number: | 3 |
| Bridge Number: | 2 |
| Crosscap Number: | 2 |
| Crossing Number: | 6 |
| Genus: | 2 |
| Hyperbolic Volume: | 4.40083 |
| Stick Number: | 8 |
| Unknotting Number: | 1 |
| Conway Notation: | [312] |
| Ab Notation: | 62 |
| Dowker Notation: | 4, 8, 10, 12, 2, 6 |
| Last Crossing: | 6 |
| Last Order: | 1 |
| Next Crossing: | 6 |
| Next Order: | 3 |
| Alternating: | alternating |
| Class: | hyperbolic |
| Fibered: | fibered |
| Prime: | prime |
| Symmetry: | reversible |
In knot theory, the 62 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 63 knot. This knot is sometimes referred to as the Miller Institute knot, because it appears in the logo[1] of the Miller Institute for Basic Research in Science at the University of California, Berkeley.
The 62 knot is invertible but not amphichiral. Its Alexander polynomial is
\Delta(t)=-t2+3t-3+3t-1-t-2,
its Conway polynomial is
\nabla(z)=-z4-z2+1,
and its Jones polynomial is
V(q)=q-1+2q-1-2q-2+2q-3-2q-4+q-5.
The 62 knot is a hyperbolic knot, with its complement having a volume of approximately 4.40083.
Ways to assemble of knot 6.2
If a bowline is tied and the two free ends of the rope are brought together in the simplest way, the knot obtained is the 62 knot. The sequence of necessary moves are depicted here: