| Abstract: |
| While it is known that a non-concyclic rhombus can form a central configuration in the planar 4-body problem, such a base is forbidden for pyramidal central configurations in the spatial 5-body problem. This paper demonstrates that this restriction does not hold for the spatial 6-body problem. We give an analytical proof of the existence of a novel class of pyramidal central configurations with a non-concyclic quadrilateral base, a structure that distinguishes them from all known spatial 5-body pyramidal central configurations. We derive several key properties associated with these new central configurations. Furthermore, we demonstrate that this new class can be utilized to construct perverse solutions in $\mathbb{R}^{3}$. We support our theoretical findings with numerical examples for each case. |
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