  In this paper, we prove the existence of a family of new non-collision
periodic solutions for the classical Newtonian $n$-body problems. In our
assumption, the $n=2l\geq4$ particles are invariant under the dihedral rotation
group $D_l$ in $\mathbb{R}^3$ such that, at each instant, the $n$ particles
form two twisted $l$-regular polygons. Our approach is variational minimizing
method and we show that the minimizers are collision-free by level estimates
and local deformations.
