In this paper we prove the existence of two new families of spatial stacked central
configurations, one consisting of eight equal masses on the vertices of a cube and six equal
masses on the vertices of a regular octahedron, and the other one consisting of twenty
masses at the vertices of a regular dodecahedron and twelve masses ...»»»»
In this paper we prove the existence of two new families of spatial stacked central
configurations, one consisting of eight equal masses on the vertices of a cube and six equal
masses on the vertices of a regular octahedron, and the other one consisting of twenty
masses at the vertices of a regular dodecahedron and twelve masses at the vertices of a
regular icosahedron. The masses on the two different polyhedra are in general different.
We note that the cube and the octahedron, the dodecahedron and the icosahedron are
dual regular polyhedra. The tetrahedron is itself dual. There are also spatial stacked central
configurations formed by two tetrahedra, one and its dual.^^^^