*Abstract.* This talk will outline properties of mappings of *k*-dimensional complex projective space, ℂ ℙ ^{k}, that are symmetric products of rational maps of ℂ ℙ ^{1}. Besides describing this construction, I will demonstrate that these products can be used to construct nontrivial maps that are strongly post-critically finite. These maps may also provide an example of an isolated Lattès map in the moduli space of degree *d* rational maps of ℂ ℙ ^{k}. I will describe the current state of this problem. This is joint work with Thomas Gauthier (Université de Picardie Jules Verne) and Benjamin Hutz (SLU).