7₁ knot

In knot theory, the 7₁ knot, also known as the septoil knot, the septafoil knot, or the (7, 2)-torus knot, is one of seven prime knots with crossing number seven. It is the simplest torus knot after the trefoil and cinquefoil.

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

$\nabla(z) = z^6 %2B 5z^4 %2B 6z^2 %2B 1, \,$

$V(q) = q^{-3} %2B q^{-5} - q^{-6} %2B q^{-7} - q^{-8} %2B q^{-9} - q^{-10}. \,$ ^[1]

References