Spatial Convex but Non-strictly Convex Double-Pyramidal Central Configurations of the $$(2n+2)$$-Body Problem

Abstract

A configuration of the N bodies is convex if the convex hull of the positions of all the bodies in $$\mathbb {R}^3$$ does not contain in its interior any of these bodies. And a configuration is strictly convex if the convex hull of every subset of the N bodies is convex. Recently some authors have proved the existence of convex but non-strictly convex central configurations for some N-body problems. In this paper we prove the existence of a new family of spatial convex but non-strictly convex central configurations of the $$(2n+2)$$ -body problem.