To obtain the moduli space of superconformal field theories associated to K3 from the parameter space discussed in the previous talk, one has to quotient by a discrete group of automorphisms. In particular, each theory has infinitely many distinct geometric interpretations which are interrelated by these automorphisms. We discuss specific automorphisms of this type, in particular a version of mirror symmetry for orbifold limits of K3, as well as a change of geometric interpretation which allows to construct superconformal field theories associated to a large family of quartic hypersurfaces, the so-called "very attractive quartics".