A square as in Exercise 31 with the letter Hat its center using translation directions given by vectors (1, 0) and (0, 1).

Describe a pattern to be used to fill the plane by translation in the two directions given by the specified vectors. Answer these questions in each case. 

a. Does the symmetry group contain any rotations? If so, through what possible angles θ where 0 < θ ≤ 180°?

b. Does the symmetry group contain any reflections? 

c. Does the symmetry group contain any nontrivial glide reflections?

 

Data from Exercise 31

A square with horizontal and vertical edges using translation directions given by vectors (1, 0) and (0, 1).

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