# Undergraduate Mathematics/The Group Theory of the Symmetries of Simple Shapes

< Undergraduate MathematicsUndergraduate Mathematics/The Group Theory of the Symmetries of Simple Shapes |

In this module, we consider the symmetries of 2D sets of points such as those pictured below.

2D

*D*_{6}symmetry – The Red Star of David2D

*D*_{24}symmetry – Ashoka Chakra, as depicted on the National flag of the Republic of India.

We ask questions like:

- Why does the combination of symmetries form a group?
- Which combinations of symmetries are the same?
- How many distinct symmetries are there for a given set?
- Which sets have the same symmetry groups?