A map is a particular form of embedding a graph on a surface which, among other things, allows one to extend the notion of "regularity" in Platonic solids to a more diverse array of objects. By abstraction to a combinatorial description we may extend this notion into higher dimensional objects. In this talk I'll give a classification of the regular generalized combinatorial maps (GCM) with one 3-dimensional facet. I'll then describe a program for discovering highly symmetric GCM with two 3-dimensional facets. In particular, this program produces a number of "chiral" GCM, i.e., GCM which are rotationally symmetric but not reflectively symmetric. This talk builds on a talk I gave in the Graduate Summer Seminar last year but does not assume your attendance there.