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 is appears in the logo[2] 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

\( V(q) = q - 1 + 2q^{-1} - 2q^{-2} + 2q^{-3} - 2q^{-4} + q^{-5}. \, [3] \)

The 6₂ knot is a hyperbolic knot, with its complement having a volume of approximately 4.40083.
References

^ Weisstein, Eric W., "Miller Institute Knot" from MathWorld.
^ Miller Institute - Home Page
^ 6 2 - Knot Atlas

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