The paper surveys highlights of the ongoing program to classify discrete
polyhedral structures in Euclidean 3-space by distinguished transitivity
properties of their symmetry groups, focussing in particular on various aspects
of the classification of regular polygonal complexes, chiral polyhedra, and
more generally, two-orbit polyhedra.Comment: 21 pages; In: Symmetry and Rigidity, (eds. R.Connelly, A.Ivic Weiss
and W.Whiteley), Fields Institute Communications, to appea