Unformatted text preview: xy . The ﬁrst two rows have been completed for you as an example. Id α β γ δ ± Id Id α β γ δ ± α α Id δ ± β γ β γ δ ± Exercise 65. If we let R θ denote counterclockwise rotation by θ degrees, H denote the ﬂip across the vertical axis, V denote the ﬂip across the horizontal axis, and F i ( i = 1 , 2) denote the diagonal ﬂips, then recall that the complete set if symmetries of the square is D 4 = { R ,R 90 ,R 180 ,R 270 ,V,H,F 1 ,F 2 } . Compute the “composition table” for D 4 as you did for S 3 above....
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 Fall '09
 RyanDaileda
 Division, Subtraction, Exponentiation, Euclidean geometry

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