Symmetry Group for Border Pattern Exploration

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Objective: Understanding the border pattern symmetry groups.

  1. List the elements of the symmetry group pma2. Is there a cyclic subgroup? What other subgroups are there?
  2. List the elements of the symmetry group p1m1. Is there a cyclic subgroup? What other subgroups are there?
  3. List the elements of the symmetry group pm11. Is there a cyclic subgroup? What other subgroups are there?
  4. List the elements of the symmetry group p1a1. Is there a cyclic subgroup? What other subgroups are there?
  5. List the elements of the symmetry group p112. Is there a cyclic subgroup? What other subgroups are there?
  6. List the elements of the symmetry group p111. Is there a cyclic subgroup? What other subgroups are there?

Handin: A sheet with answers to all questions.