We consider planar central configurations of the Newtonian 2n-body problem consisting in two twisted regular n-gons of equal masses. We prove the conjecture that for n=5 all convex central configurations of two twisted regular n-gons are strictly convex.
Barrabés, E., Cors, J. On strictly convex central configurations of the 2n-body problem. "Journal of dynamics and differential equations", Desembre 2019, vol. 31, n. 4, p. 2293–2304.