Double-Antiprism Central Configurations of the 3n-Body Problem

In this paper we study numerically a new type of central configurations of the 3n-body problem with equal masses which consist of three n-gons contained in three planes z=0 and z= ±β ≠ 0. The n-gon on z=0 is scaled by a factor α and it is rotated by an angle of Π /n with respect to the ones on z= ±β. In this kind of configurations, the masses on the planes z=0 and z=β are at the vertices of an antiprism with bases of different size. The same occurs with the masses on z=0 and z=-β. We call this kind of central configurations double-antiprism central configurations. We will show the existence of central configurations of this type. © 2012 Springer Basel AG.