  Consider four point particles with equal masses in the euclidean space,
subject to the following symmetry constraint: at each instant they are
symmetric with respect to the dihedral group $D_2$, that is the group generated
by two rotations of angle $\pi$ around two orthogonal axes. Under a homogeneous
potential of degree $-\alpha$ for $0<\alpha<2$, this is a subproblem of the
four-body problem, in which all orbits have zero angular momentum and the
configuration space is three-dimensional. In this paper we study the flow in
McGehee coordinates on the collision manifold, and discuss the qualitative
behavior of orbits which reach or come close to a total collision.
