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10. If r , 2, and r3 represent rotations from D,, and fi, f2, and f3 represent reflections from D,, determine whether r,2 fir3 f2 f3 3 is a rotation or a reflection. 11. Find elements A, B, and C in D, such that AB = BC but A # C. (Thus, "cross cancellation" is not valid.) 12. Explain what the following diagram proves about the group D F R360/17 n - 2 F 13. Describe the symmetries of a nonsquare rectangle. Construct the corresponding Cayley table. 14. Describe the symmetries of a parallelogram that is neither a rect- angle nor a rhombus. Describe the symmetries of a rhombus that is not a rectangle. 15. Describe the symmetries of a noncircular ellipse. Do the same for a hyperbola. 16. Consider an infinitely long strip of equally spaced H's: . . HHHH . . . Describe the symmetries of this strip. Is the group of symmetries of the strip Abelian? 17. For each of the snowflakes in the figure, find the symmetry group