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There aren't any. Hausdorff spaces are sober spaces. If $X, Y$ are sober, then every locale map $\mathcal{O}(Y) \to \mathcal{O}(X)$, i.e., every poset map between their topologies that preserves finite meets and arbitrary joins, arises from a uniquely determined continuous map $X \to Y$. It follows that a poset isomorphism $\mathcal{O}(X) \cong \mathcal{O}(Y)$, being a locale isomorphism, arises from a homeomorphism between the spaces.