  Let $F, G \in \mathbb{Z}[X, Y]$ be binary forms of degree $\geq 3$ with
automorphism groups isomorphic to the dihedral group of cardinality $6$ or
$12$. We characterize exactly when $F$ and $G$ have the same value set, i.e.
$F(\mathbb{Z}^2) = G(\mathbb{Z}^2)$.
