The relationship between K3 surfaces and singular affine structures on $S^{2}$ is of very general origin. Starting with a projective analytic Calabi-Yau manifold $X$ over a complete non-archimedean local field $K$ one can canonically construct a PL manifold $Sk(X)$ called the skeleton of $X$. If $X$ is a generic K3 surface then $Sk(X)$ is $S^{2}$. We discuss skeleta in Section 6.6. The group of birational automorphisms of $X$ acts on $Sk(X)$ by integral PL transformations. For $X=K3$ we obtain an action of an arithmetic subgroup of $SO(1,18)$ on $S^{2}$. Further examples should come from Calabi-Yau manifolds with large groups of birational automorphisms.