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E21. Equiangular and Equilateral Polygons

A polygon is equiangular if all of its angles are equal. In particular, if the polygon has n sides, each angle measures (n - 2) * 180 / n degrees. A polygon is equilateral if all of its sides have the same length. It can be shown very easily that every equiangular triangle is equilateral. Of course, it is not true that every equiangular quadrilateral is equilateral. Any rectangle that is not a square provides a counterexample. Show that for every n > 3 there exists an equiangular n-gon that is not equilateral.

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