Stacked Central Configurations for Newtonian N+4-Body Problems
  In this paper,we study spatial central configurations where N bodies are at the vertices of a regular N-gon $T$ and the other 4 bodies are symmetrically located on the straight line that is perpendicular to the plane that contains $T$ and passes through the center of $T$.We study the necessary conditions about masses for the bodies which can form a central configuration and show the existence of central configurations for Newtonian N+4-body problems. 
Furong Zhao and Shiqing Zhang
math-ph math.CA math.MP