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Central configurations of nested regular polyhedra for the spatial \(2n\)-body problem. (English) Zbl 1146.70007

Summary: We consider \(2n\) masses located at vertices of two nested regular polyhedra with the same number of vertices. Assuming that the masses in each polyhedron are equal, we prove that for each ratio of the masses of the inner and the outer polyhedra there exists a unique ratio of the length of the edges of the inner and the outer polyhedra such that the configuration is central.

MSC:

70F10 \(n\)-body problems
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