A new central configuration in the planar NN-body problem

B. Elmabsout [C. R. Acad. Sci. 329, Serie II (1991)] has proved that a central configuration of 2n2n bodies located on two concentric regular nn-gons exists iff the polygons are homotetic or similar with an angle equal to πnπn and the masses on the same polygon are equal. In this paper we study the existence of a planar central configuration which consists of 3n3n bodies also situated on two regular polygons, the "interior" nn-gon with equal masses and the "exterior" 2n2n-gon with masses of two quantities, and these quantities alternate.