# Amphicheiral knot polynomials — H2

Let \(K\subset S^3\) be a smooth oriented knot admitting an orientation-reversing diffeomorphism \(h:S^3\to S^3\) with \(h^2=\operatorname{id}\), \(h(K)=K\), and \(h|_K\) preserving orientation.
There exists \(\varphi\in\mathbb Z[w]\) such that
\[
\nabla_K(z)=\varphi(z^2)^2.
\]
Here \(\nabla_K\) is the Conway polynomial normalized by \(\nabla_{\rm unknot}=1\).