  We apply the version of P\'{o}lya-Redfield theory obtained by White to count
patterns with a given automorphism group to the enumeration of strong dichotomy
patterns, that is, we count bicolor patterns of $\mathbb{Z}_{2k}$ with respect
to the action of $\Aff(\mathbb{Z}_{2k})$ and with trivial isotropy group. As a
byproduct, a conjectural instance of phenomenon similar to cyclic sieving for
special cases of these combinatorial objects is proposed.
