In this talk, I will discuss recent joint work with Alexeev-Engel-Schaffler that provides explicit, combinatorial descriptions of stable degenerations of numerically polarized Enriques surfaces of degree 2. We show that this can be identified with a semitoroidal compactification of the Hodge-theoretic period domain, leveraging Alexeev-Engel’s seminal work on compactifications of moduli spaces of K3 surfaces via integral-affine geometry. In this work, we generalize the classical theory of “folding” Dynkin diagrams and the induced involutions on integral affine spheres and extend Alexeev-Thompson’s theory of toric ADE surfaces to types B and C to classify boundary strata of the stable pair compactification.