7 2 knot

In knot theory, the Pentatwist knot, also known as the five-twist knot, or the 7₂, is one of seven prime knots with crossing number seven. It is the fifth twist knot.

Its Alexander polynomial is

${\displaystyle \Delta (t)=3t-5+3t^{-1},\,}$

its Conway polynomial is

${\displaystyle \nabla (z)=3z^{2}+1,\,}$

and its Jones polynomial is

${\displaystyle V(q)=-q^{-8}+q^{-7}-q^{-6}+2q^{-5}-2q^{-4}+2q^{-3}-q^{-2}+q^{-1}.\,}$^[1]