#### Title

#### Publication Year

1996

#### Keywords

Crystallography, physics, crystals, mathematics, molecules

#### Disciplines

Atomic, Molecular and Optical Physics | Mathematics | Physical Sciences and Mathematics | Physics

#### Abstract

Crystallography is a branch of physics that studies the properties of crystals. The atoms that make up a crystal molecule and the actual crystal molecules are arranged in a systemic, infinitely repeating pattern. These patterns can be explained using mathematics.

This paper will explore all of the patterns or crystallographic groups that are possible in the second-dimension. After determining the pattern in the second-dimension, it is easy to apply to the third-dimension. The defining characteristic of each pattern is that each one is made up of distinct combinations of the various plane isometries. These will be discussed in more detail later. But, before plane isometries can be discussed, group theory must first be explained because each pattern can be classified according to the plane isometries that it has and these isometries form an algebraic group. After those concepts are established, we may then begin the classification of the different possible patterns or crystallographic groups.

#### Department 1 Awarding Honors Status

Physics

#### Department 2 Awarding Honors Status

Mathematics

#### Recommended Citation

Young, M.
(1996).
*Crystallographic Groups* (Undergraduate honors thesis, University of Redlands).
Retrieved from https://inspire.redlands.edu/cas_honors/675