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

2D 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?