Frieze Exercises

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  1. Copy (or print out) these simple frieze patterns, and mark all symmetries for each pattern. That is, identify and mark all translations, rotations, reflections and glide-reflections if present.
    1. Ladder.svg
    2. Zigzag.svg

    3. Moons.svg

  2. Identify the symmetry group for each of these frieze patterns:
    1. Ngaru.svg
    2. Stlcb-pm11-4.jpg
    3. Bear-tracks.svg
    4. Dna.jpg
  3. Use this motif to draw seven frieze patterns, one with each symmetry group: Simple-motif.svg
  4. Consider the four colorful strip patterns that Escher found in Ravello, Italy (Designs from Ravello).
    For each pattern, identify which symmetries are present (all have translational symmetry, but state if the pattern has rotational, refelctional and/or glide reflectional symmetry). Use this information to decide which frieze symmetry group it has. You can ignore colors.
  5. Koloman Moser, Lachzug, 1899
    Koloman Moser was an Austrian art deco artist who designed patterned textiles. What is the symmetry group of the frieze pattern shown here? See Visions of Symmetry Page 42-43 for a better picture and a discussion of Moser's relationship to Escher.
  6. Draw four patterns with the symmetry group pma2. Make them look as different as possible. Be creative.
  7. In a frieze pattern with a glide reflection, explain why the glide reflection is always half the length of the shortest translation.
  8. Explain why a frieze pattern can have only 180° rotations.
    1. What frieze symmetry group do you get if you write a row of A’s? B’s? Answer this for all 26 capital letters by listing the letters that correspond to each symmetry group. Use the alphabet below: Alphabet.svg
    2. Compare with your answer to Rosette Exercises#alphabet. Do letters which had the same rosette symmetry group make frieze patterns with the same symmetry group?
  9. László Fejes Tóth studied symmetry groups extensively. His illustrations of the seven Frieze patterns are shown here, along with his names for their symmetry groups (the F's with numbers attached).
    1. Make a table showing the correspondence between the Fejes Tóth names and the IUC names.
    2. What does the subscript 2 signify in the Fejes Tóth names?

    Fejes-toth-frieze-1.jpg Fejes-toth-frieze-2.jpg

  10. Watch this Fruit by the Foot video, by Vi Hart. She discusses a Frieze pattern which is stamped on the candy. What pattern is it?

Instructor:Frieze Exercises Solutions (restricted access)