Stacked central configurations for Newtonian -body problems

We show the existence of spatial central configurations for the N + 2 p -body problems. In such a configuration, N bodies are at the vertices of a regular N -gon T ; 2 p bodies are symmetric with respect to the center of T , and located on the straight line which is perpendicular to the regular N -gon T and passes through the center of T . The masses located on the vertices of the regular N -gon are assumed to be equal; the masses located on the same line and symmetric with respect to the center of T are equal.