Biconnected planar non-maximal reconstruction conjecture

Let $G$ be a planar biconnected graph with minimum degree $\delta(G)\geq 3$, and suppose that $G$ is not maximal planar. Let $\mathcal{D}(G)$ be its vertex-deletion deck. Biconnected planar reconstruction conjecture. The graph $G$ is reconstructible from its deck; moreover, there is a polynomial-time reconstruction algorithm that recovers the edge count and degree multiset, selects a minimum-degree vertex $v$ with $\deg(v)\leq 5$, identifies candidate neighborhoods using degree and triangle constraints, and verifies the correct candidate by exact deck equality. The claim is motivated by computational experiments, while the supplied context does not provide a proof for the stated class or algorithmic bound.