ABSTRACT
Geometry is the study of those properties of a set S that remain invariant when the elements of S are subjected to the transformations of some transformation group.
Felix Klein (1849-1925)
Father of Transformational Geometry
A symmetry of a plane figure F is an isometry that fixes F. If F is an equilateral triangle with centroid C, for example, there are six symmetries of F, one of which is the rotation ρC,120. In this chapter we observe that the set of symmetries of a plane figure is a “group” with respect to composition of isometries. The structure of these groups, called symmetry groups, faithfully encodes the symmetries of plane figures and their interrelationships.
