6₂ knot
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,[1] because it appears in the logo[2] of the Miller Institute for Basic Research in Science at the University of California, Berkeley.
6₂ knot | |
---|---|
![]() | |
Arf invariant | 1 |
Braid length | 6 |
Braid no. | 3 |
Bridge no. | 2 |
Crosscap no. | 2 |
Crossing no. | 6 |
Genus | 2 |
Hyperbolic volume | 4.40083 |
Stick no. | 8 |
Unknotting no. | 1 |
Conway notation | [312] |
A-B notation | 62 |
Dowker notation | 4, 8, 10, 12, 2, 6 |
Last /Next | 61 / 63 |
Other | |
alternating, hyperbolic, fibered, prime, reversible |
The 62 knot is invertible but not amphichiral. Its Alexander polynomial is
its Conway polynomial is
and its Jones polynomial is
The 62 knot is a hyperbolic knot, with its complement having a volume of approximately 4.40083.
Surface
- Surface of knot 6.2
Example
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:
- From a bowline (ends connected) to the 6₂ knot.