Frieze Group Exploration

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Discover the possible frieze groups.


  • Two copies of the Inca strip patterns, one printed on paper and one on a transparency.
  • Scissors


  1. Cut the transparency sheet into strips, and use them to find and mark all symmetries of the five inca patterns.
  2. Which two of the five have the same symmetry group?
  3. Draw a few new frieze patterns.
  4. Draw these if you can:
    • A frieze pattern with exactly one reflection symmetry.
    • A frieze pattern with a glide reflection and at least one rotation.
    • A frieze pattern with rotation symmetry, and exactly one reflection.
  5. Find a type of Frieze symmetry not shown among the inca patterns, and not shown in question 4. Draw an example of it.

Handin: Answers to the questions and the paper of inca strip patterns, marked with symmetries.