Frieze patterns

Q 1. A frieze pattern has one and only one direction of translation. The translation isometry is denoted by T. As we have noticed in lectures the symmetry group of the fundamental pattern consists of all powers of T and is thus isomorphic to which group? Q 2. Now use Lemma F from your lecture notes to prove the following result: Proposition a) If there is a rotation R present in the symmetry group of any frieze pattern then R is a turn of magnitude 0 or ¼. b) If there is a re°ection m present in the symmetry group of any frieze pattern then m is either parallel or perpendicular to the direction of T. Q 3. A turn of magnitude 0 is equal to what element of the group? Q 4... click for more

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