  We present a rigid isotopy classification of irreducible sextic curves in
$\mathbb{RP}^2$ which have non-real ordinary double points as their only
singularities. Our approach uses periods of K3 surfaces and V. Nikulin's
classification of involutions with condition on unimodular lattices. The
classification obtained generalizes Nikulin's rigid isotopy classification of
non-singular sextics in $\mathbb{RP}^2$.
