  Let $K$ be a knot type for which the quadratic term of the Conway polynomial
is nontrivial, and let $\gamma: \mathbb{R}\to \mathbb{R}^3$ be an analytic
$\mathbb{Z}$-periodic function with non-vanishing derivative which
parameterizes a knot of type $K$ in space. We prove that there exists a
sequence of numbers $0\leq t_1 < t_2 < ... < t_6 < 1$ so that the polygonal
path obtained by cyclically connecting the points $\gamma(t_1), \gamma(t_2),
..., \gamma(t_6)$ by line segments is a trefoil knot.
