2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168483W. Thurston proved that to a triangulation of the sphere of non-negative combinatorial curvature, one can associate an element in a certain lattice over the Eisenstein integers such that its orbit is a complete invariant of the triangulation. In this paper, we show that this association can be obtained naturally by using Type III degenerations of K3 surfaces.37 pagesAlgebraic Geometrytext