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A circle, rotated through an angle measuring any real value in the interval [0, 360 degrees) or [0, 2*pi radians) and remain symmetrical. The order of symmetries is therefore the continuum, C - a number that is uncountably infinite (as opposed to countably infinite). No other 2-dimensional shape can match that.

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The perimeter of a circle measured from the centre is the same length no matter where the measurement is taken.

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Q: Why is a circle the shape with the most rotational symmetry?
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