6₂ knot

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, twist

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 is invertible but not amphichiral. Its Alexander polynomial is

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

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.