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We prove that the billiard claimed to be a possible counterexample to theBirkhoff-Poritsky conjecture is actually not a counterexample. We also showthat for a billiard in a table obtained by the string construction over anyconvex polygon, this polygon is a core of the billiard dynamics.

A challenger to elliptic billiards fails: String construction over convex polygons and the Birkhoff--Poritsky conjecture