  The set of transverse homoclinic intersections for a saddle-focus equilibrium
in the planar equilateral restricted four-body problem admit certain simple
homoclinic orbits which form the skeleton of the complete homoclinic
intersection -- or homoclinic web. In the present work, the planar restricted
four-body problem is viewed as an invariant subsystem of the spatial problem,
and the influence of this planar homoclinic skeleton on the spatial dynamics is
studied from a numerical point of view. Starting from the vertical Lyapunov
families emanating from saddle focus equilibria, we compute the stable/unstable
manifolds of these spatial periodic orbits and look for intersections between
these manifolds near the fundamental planar homoclinics. In this way, we are
able to continue all of the basic planar homoclinic motions into the spatial
problem as homoclinics for appropriate vertical Lyapunov orbits which, by the
Smale Tangle theorem, suggest the existence of chaotic motions in the spatial
problem. While the saddle-focus equilibrium solutions in the planar problems
occur only at a discrete set of energy levels, the cycle-to-cycle homoclinics
in the spatial problem are robust with respect to small changes in energy.
