Frieze Marking Exploration

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Objective: Learn to recognize symmetries of frieze patterns.


  • Two copies of File:Blocky.pdf, one printed on paper and one on a transparency.
  • Scissors


  • Cut the transparency into eight strips as indicated.
  • First test for vertical and horizontal reflection symmetry. You can fold up the paper and check if there is a match.
  • For each strip pattern on the paper, use the corresponding transparency strip as an overlay to test for the remaining symmetries:
    • Test for glide-reflections: Can you make the frieze pattern match up if you reflect the trip and slide it horizontally?
    • Test for rotational symmetry: Does the frieze look the same if you turn it through 180 degrees?

Answer the following questions:

  1. On the paper, mark all symmetries for each pattern:
    1. Mark the length of the translation.
    2. Mark any reflectional symmetry by drawing the mirror lines.
    3. If there is a glide reflection, mark the length of the translation and label that arrow with a G.
    4. Mark any centers of rotation with a diamond.
  2. Identify the frieze group for each pattern.
  3. What is going on with pattern #8?

Handin: The paper of strip patterns, marked with symmetries and the frieze groups.