1. Contemporary Abstract Algebra
SEVENTH EDITION
Joseph A. Gallian

2. Chapter 1: Introduction to Groups
Symmetries of a Square
The Dihedral Groups

3. 1.1 Symmetries of a Square

4. The Square 1/3

5. The Square 2/3

6. The Square 3/3

7. Multiplication

8. The Dihedral Group
The analysis carried out above for a square can similarly be done for an equilateral triangle or regular pentagon or, indeed,
any regular n-gon (n ≥ 3). The corresponding group is denoted by
and is called the dihedral group of order 2n.

9. The Dihedral Group This group has 2n elements n rotations, namely
n reflection:
Example: