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TOT 316 1991 Autumn A S2 divide plane into polygons, rotation

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June 9, 2024
rotationcombinatoricscombinatorial geometrygeometrygeometric transformation

Problem Statement

Is it possible to divide the plane into polygons so that each polygon is transformed into itself under some rotation by 360/7360/7 degrees about some point? All sides of these polygons must be greater than 11 cm. (A polygon is the part of a plane bounded by one non-self-intersect-ing closed broken line, not necessarily convex.)
(A. Andjans, Riga)