In this paper we prove, for all p ≥ 2, the existence of central configurations of the pn-body problem where the masses are located at the vertices of p nested regular polyhedra having the same number of vertices n and a common center. In such configurations all the masses on the same polyhedron are equal, but masses on different polyhedra could be different. © Springer Science+Business Media B.V. 2010.
- N-body problems
- Nested regular polyhedra
- Spatial central configurations