Frieze Names Exploration

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Time-30.svg

Objective:

Learn alternate names for the seven Frieze groups

John Conway is one of the most famous mathematicians of this era. He drew these seven “feet” pictures:

hop Hop.gif
jump Jump.gif
sidle Sidle.gif
spinhop Spinhop.gif
spinjump Spinjump.gif
spinsidle Spinsidle.gif
step Step.gif
  1. Find the symmetries for each of Conway’s pictures and figure out which IUC names correspond to Conway’s names. Make a table showing the correspondence between the IUC names and the Conway names. (For example, the “jump” corresponds to p1m1).
  2. Get out of your chair and perform all seven of the Conway steps. Which is the hardest?

Now run the computer program Kali.

  1. Play around with the different frieze symmetry groups. Make one frieze pattern you’re proud of and print it out. Write the IUC name of the symmetry group you used on the printed pattern.
  2. Make a list of all seven IUC names and the corresponding names used by Kali.

Handin: A sheet with answers to the questions and your printed Frieze pattern