Polybius Square | Breakthrough: The Ideas That Changed the World

The eight symmetries of a square form a group that we will call Sq, generated by a 90° anticlockwise rotation r, and a horizontal flip f. A Cayley diagram is shown below.1243(a) For each axis of reflection, express the symmetry across it in terms of r and f.(b) Find all minimal generating sets. [Hint: There are 12.](c) Let s = f and t = r³f = fr. Draw a Cayley diagram using s and t as generators.(d) Write a presentation of the form Sq = (r, f...).(e) Write a presentation of the form Sq = (s, t