2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71699In this paper we propose a way to construct an analytic space over a non-archimedean field, starting with a real manifold with an affine structure which has integral monodromy. Our construction is motivated by the junction of Homological Mirror conjecture and geometric Strominger-Yau-Zaslow conjecture. In particular, we glue from "flat pieces" an analytic K3 surface. As a byproduct of our approach we obtain an action of an arithmetic subgroup of the group $SO(1,18)$ by piecewise-linear transformations on the 2-dimensional sphere $S^2$ equipped with naturally defined singular affine structure.80 pages, 8 figuresAlgebraic GeometrySymplectic Geometry14J32; 14G22; 37J35text