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44. WINDMILLS AND GROUPS The illustrated windmill has four sails arranged at 90° angles. If the sails are rotated through 0°, 90°, 180° or 360° they assume the ‘same’ position. If R denotes a clockwise rotation through 90°, we can say that the transformations R0 =I (the identity), R, R2 and R3 all map this position of the sails to itself. Mathematically this corresponds to a cyclic group generated by R and such that R4 = I. This group has order 4. What can you say about this other windmill and its group?
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