  We study the conditions that favour boxiness of isodensities in the face-on
views of orbital 3D models for barred galaxies. Using orbital weighted profiles
we show that boxiness is in general a composite effect that appears when one
considers stable orbits belonging to several families of periodic orbits. 3D
orbits that are introduced due to vertical instabilities, play a crucial role
in the face-on profiles and enhance their rectangularity. This happens because
at the 4:1 radial resonance region we have several orbits with boxy face-on
projections, instead of few rectangular-like x1 orbits, which, in a fair
fraction of the models studied so far, are unstable at this region. Massive
bars are characterized by rectangular-like orbits. However, we find that it is
the pattern speed that affects most the elongation of the boxy feature, in the
sense that fast bars are more elongated than slow ones. Boxiness in
intermediate distances between the center of the model and the end of the bar
can be attributed to x1v1 orbits, or to a combination of families related to
the radial 3:1 resonance.
