Chapter 3: WHICH ISOMETRIES DO IT?



This chapter is devoted to isometry reconstruction, which is rather crucial for a 'dynamic' understanding of wallpaper patterns. The reconstruction of isometries between any two congruent sets is methodically reduced to the determination of isometries between two equal straight line segments. The presentation is totally geometrical, but the overall development of the topic culminates naturally in a brief introduction to cyclic and dihedral groups.