5) (a) Write down (or use the algorithm and simplify) a set of generators and relations for the wallpaper group 112. The diagram above shows a tiling by fundametal domains for this group. Choose and indicate (in different colours) reflection lines for each of your generators. Hence draw the "Cayley graph for the group on the diagram. (You need only draw enough that the pattern is clear.) (b) How many 3-colourings are there of this group? (Explain your reasoning.) 1 5) (a) Write down (or use the algorithm and simplify) a set of generators and relations for the wallpaper group 112. The diagram above shows a tiling by fundametal domains for this group. Choose and indicate (in different colours) reflection lines for each of your generators. Hence draw the "Cayley graph for the group on the diagram. (You need only draw enough that the pattern is clear.) (b) How many 3-colourings are there of this group? (Explain your reasoning.) 1