Existence of Really Perverse Central Configurations in the Spatial $N$-Body Problem

TL;DR

This paper constructs explicit examples of spatial really perverse central configurations in the Newtonian N-body problem, demonstrating their existence for N=27 to 55, expanding known results beyond the planar case.

Contribution

It provides the first explicit constructions of spatial really perverse central configurations for N between 27 and 55, extending previous planar results.

Findings

Existence of spatial really perverse central configurations for N=27 to 55.

Explicit examples of such configurations are constructed.

These configurations satisfy central equations for two different mass distributions.

Abstract

We construct explicit examples of really perverse central configurations in the spatial Newtonian $N$-body problem. A central configuration is called really perverse if it satisfies the central configuration equations for two distinct mass distributions having the same total mass. While such configurations were previously known only in the planar case for large $N$, we prove the existence of spatial really perverse central configurations for $N=27,\dots,55$.