Dual Billiards, Fagnano Orbits, and Regular Polygons

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In this article we consider the dual version of two results on polygonal billiards. We begin by describing these original results. The first result is about the dynamics of the so-called pedal map related to billiards in a triangle P. The three altitudes of P intersect the opposite sides (or their extensions) in three points called the feet. These three points form the vertices of a new triangle Q called the pedal triangle of the