Dimitris Vartziotis and Joachim Wipper, On the construction of regular polygons and generalized Napoleon vertices,
Forum Geometricorum, 9 (2009) 213--223.

Abstract:   An algebraic foundation for the derivation of geometric construction schemes transforming arbitrary polygons with n vertices into k-regular n-gons  is given. It is based on circulant polygon transformations and the  associated eigenpolygon decompositions leading to the definition of  generalized Napoleon vertices. Geometric construction schemes are derived exemplarily for different choices of n and k.

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