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A regular polygon is a polygon that is both equilateral (all sides are equal) and equiangular (all interior angles are equal). The simplest polygons include triangles (three sides), quadrilaterals (four sides), and pentagons (five sides). Examples of regular polygons are an equilateral triangle and a square. Constructing regular polygons with only a ruler and compass has been a challenge since antiquity, with notable progress made by mathematicians like Carl Friedrich Gauss.12

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  1. polygon
  2. Euclidean geometry

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