  Consider n=2l>=4 point particles with equal masses in space, subject to the
following symmetry constraint: at each instant they form an orbit of the
dihedral group D_l, where D_l is the group of order 2l generated by two
rotations of angle pi around two secant lines in space meeting at an angle of
pi/l. By adding a homogeneous gravitational (Newtonian) potential one finds a
special $n$-body problem with three degrees of freedom, which is a kind of
generalisation of Devaney isosceles problem, in which all orbits have zero
angular momentum. In the paper we find all the central configurations and we
compute the dimension of the stable/unstable manifolds.
