3. In this problem, we will define two variations of the Coin2 group from lecture. We will consider two types of tiles, and declare the following to be the -home state" of each: 123 \begin{tabular}{|l|l} \hline 1 & 2 \\ \hline 4 & 3 \\ \hline \end{tabular} Our first group is Coin 3=c,t, where c "cyclicaly shifts" the entries, and t "toggles" the color of the leftmost square: Our second group is Box2=r,s, where r "rotates" the squares counterclockwise, and s "swaps" the squares on the top row. Note that the square tiles don't actually need to be shaded. An alternate way to denote the colors of the 31 dominos is to underline any number with a black background. For example, using this convention, the "home state" would be written 123 . (a) Both of these groups have 24 actions. Draw a Cayley diagram for each, with the nodes labeled by configurations. It is helpful to know that the one for Coin 3 can be arranged on a truncated cube, whose skeleton is shown below (left). A Cayley diagram for Box2 can be arranged on a truncated octahedron, shown below (right). But the "home state" at the yellow node. (b) Write down a presentation for each of these groups. (c) Are these groups isomorphic? Justify your