A triangulated K3 surface with the minimum number of vertices

Any combinatorial triangulation of a K3 surface requires at least 16 vertices, and it has to contain all possible 163 triangles if there are exactly 16 vertices. In this paper we present such a 16-vertex K3 surface. It is invariant under the group AGL(1, F16)≅F4⊕2 ⋊ C15 of order 240 acting transitively on the set of oriented edges. In close relation with the triangulation we find the classical Kummer configuration 166. This 16-vertex triangulation is a tight triangulation, leading to the corollary that there exists a tight polyhedral embedding of a K3 surface into the Euclidean space E15.