// Workers AI · dad joke modeIs a 62 knot tied up about its speed?

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

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 of the Miller Institute for Basic Research in Science at the University of California, Berkeley.

The 6₂ knot can be represented with the following parametric equation :

${\begin{aligned}x&=\cos(2\phi )\\y&=\cos(7\phi +\pi /4)\\z&=\cos(\phi +1.9065)+\cos(7\phi +5.01637)\end{aligned}}$

with $0\leq \phi \leq 2\pi$.

The 6₂ knot is invertible but not amphichiral. Its Alexander polynomial is

$\Delta (t)=-t^{2}+3t-3+3t^{-1}-t^{-2},\,$

its Conway polynomial is

$\nabla (z)=-z^{4}-z^{2}+1,\,$

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.

Surface

• 
  Surface of knot 6.2

Example

Ways to assemble of knot 6.2

• Example 1
• Example 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