Can one find a collection of sixteen points and sixteen planes in our three dimensional space, such that each of the planes contains precisely six points and each of the points is contained in precisely six planes? It is not very hard to convince oneself that the answer is "yes". On the other hand, such collections are intimately related to the geometry of so-called Kummer-K3-surfaces, fascinating objects that have been studied in detail in mathematics. This talk aims to shed some light on those K3-surfaces: Their origin in geometric optics and their relation to the above mentioned sixteen-six configurations, their geometric properties, and their use in modern theoretical physics, that is in string theory and conformal field theory.