Twisted stacked central configurations for the spatial nine-body problem

In this article, we study the existence of the twisted stacked central configurations for the nine-body problem. More precisely, the position vectors x 1, x 2, x 3, x 4 and x 5 are at the vertices of a square pyramid Σ; the position vectors x 6, x 7, x 8 and x 9 are at the vertices of a square Π; the square (x 1, x 2, x 3, x 4) and the square (x 6, x 7, x 8, x 9) have twisted angle π/4.