Double pyramidal central configurations of Newtonian ([formula omitted]+2)-body problem

Abstract

For double pyramidal central configurations of the Newtonian (N+2)-body problem where N point particles are positioned at the vertices of a regular N-polygon, and the (N+1)-th and (N+2)-th point-particles are positioned the opposite sides of the plane containing the polygon, and the two point particles are located on a line, which is perpendicular to the regular N-polygon, we obtain some properties of the positions, masses and values of N of these N+2 point-particles