New classes of spatial central configurations for the n+3n+3-body problem

In this paper, we show the existence of new families of spatial central configurations for the n+3n+3-body problem, n≥3n≥3. We study spatial central configurations where nn bodies are at the vertices of a regular nn-gon TT and the other three bodies are symmetrically located on the straight line that is perpendicular to the plane that contains TT and passes through the center of TT. The results have simple and analytic proofs.