Symmetry and Perfection of Form

Abstract

Objects in space are here considered from the point of view of geometrical symmetry. Accordingly, only their shape or form is important, and their size or position in space may be ignored. By comparing the symmetry of a given object with that of nearby objects of the same kind, we can identify those objects that are 'perfect' of their kind in a precise, technical sense. Among convex polyhedra with given incidence structure, there are exactly nine instances of such perfection of form.