In this Letter we study the necessary conditions for the masses of the two
layer nested regular polygon central configurations in R-3. If the masses a
t the corresponding vertices of the upper nested regular polygons have the
same ratio, and the masses at the corresponding vertices of the lower neste
d regular polygons the same ratio, then masses at the vertices of each regu
lar polygon are equal. (C) 2001 Published by Elsevier Science B.V.