Symmetry Group for Border Pattern Exploration

Objective: Understanding the border pattern symmetry groups.

1. List the elements of the symmetry group MG. Is there a cyclic subgroup? What other subgroups are there?

2. List the elements of the symmetry group M1. Is there a cyclic subgroup? What other subgroups are there?

3. List the elements of the symmetry group 1M. Is there a cyclic subgroup? What other subgroups are there?

4. List the elements of the symmetry group 1G. Is there a cyclic subgroup? What other subgroups are there?

5. List the elements of the symmetry group 12. Is there a cyclic subgroup? What other subgroups are there?

6. List the elements of the symmetry group 11. Is there a cyclic subgroup? What other subgroups are there?

Handin: A sheet with answers to all questions.