Professor Egon Schulte Mathematics, Northeastern University Symmetry of geometric figures is among the most frequently recurring themes in science. In a sequence of three talks (given by Egon Schulte, Anthony Cutler and Daniel Pellicer-Covarrubias, in this order), we shall discuss symmetry of discrete geometric structures, namely polytopes, polyhedra, and related polytope-like figures, with an emphasis on the structures with the highest degree of symmetry. The journey begins with the most famous geometric figures, the Platonic solids, and will lead us from the euclidean regular polytopes and their symmetry groups, to purely combinatorial structures, abstract regular polytopes, and their automorphism groups.