Investigation Of Plane Symmetry In Lattice Designs

Abstract

The purpose of this research project is to analyze the scholarly article The Plane Symmetry Groups: Their Recognition and Notation by Doris Schattschneider. In this article, Schattschneider discusses an application of abstract algebra which is useful in art as well as crystallography: frieze groups and wallpaper groups. I was interested in pursuing this topic because it combines mathematics with its applications, particularly with my own interest in chemistry. The article provides a compiled resource of terminology and rules of these groups, but not one which was easily accessible to undergraduate students. In my research, I elaborated on the descriptions of certain types of periodic patterns to add to the accessibility, and analyzed a few designs to prove their classification based on the rules from Schattschneider's article. I found that this resource provided a good source of rules for which mathematical proofs could be based, and proved the classification of two different periodic plane designs.