The skeleton of a Berkovich analytic space is a subspace onto which the whole space deformation retracts. For an abelian variety, the skeleton is a real torus with an "integral structure". I will discuss "faithful tropicalization" of abelian varieties in terms of non-archimedean and tropical theta functions. The solution relies on interesting combinatorial facts about lattices, matroids, and Voronoi decompositions. I will assume very little from my previous (November 18) talk. This talk is based on joint projects with Tyler Foster, Joe Rabinoff, and Alejandro Soto.