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Which Regular Polygon Can Be Drawn Using Rotations?

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Oddman answered
Every regular polygon has rotational symmetry. That is, the polygon looks the same if it is rotated by the amount of the central angle.
In that sense, every regular polygon can be drawn using rotations.
  Pick a point on a circle. Mark it.
  Rotate the circle by the amount of the central angle of the polygon of interest.
  Mark the point that is now at the location where the previous point was.
  Draw a line segment to the point previously marked.
  Repeat until the circle has been rotated 360 degrees.

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