Equiangular polygon

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Equiangular hexagons

An equiangular polygon in the geometry of a polygon of the Euclidean plane in which all interior angles are equal. Equiangular polygons are to be distinguished from equilateral polygons , in which the polygon sides are all of the same length. A polygon that is both equiangular and equilateral is called a regular polygon .


A polygon is called equiangular if the interior angles of the polygon are all the same size, that is, if

applies. Since the inside and outside angles at the corners of a polygon add up to 180 °, all outside angles are equivalent to this in an equiangular polygon .


  • An equilateral triangle is just an equilateral triangle with interior angles to and exterior angles to .
  • An equiangular quadrilateral is a rectangle with inside and outside angles each .
  • A regular polygon is an equiangular polygon that is also equilateral.


  • A tangent polygon that is equiangular is always equilateral and therefore regular.
  • A chord polygon is equiangular if and only if the side lengths alternate between two values.
  • A simple, that is, a non- overturned , equiangular polygon is always convex . Since the sum of the angles in a simple corner always results, measure all interior angles in a simple equiangular polygon
and all exterior angles
  • In simple equiangular polygons, Viviani's theorem also applies , according to which the sum of the distances from any point inside the polygon to the sides of the polygon is independent of the position of the point.

Individual evidence

  1. Michael De Villiers: Equiangular cyclic and equilateral polygons circumscribed . In: Mathematical Gazette . No. 95 , 2011, pp. 102-107 .

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