New central configurations of the (n+1)-body problem

In this article we study central configurations of the (n+1)-body problem. For the planar (n+1)-body problem we study central configurations performed by n≥2 bodies with equal masses at the vertices of a regular n-gon and one body with null mass. We also study spatial central configurations considering n bodies with equal masses at the vertices of a regular polyhedron and one body with null mass.