  We present families, and sets of families, of periodic orbits that provide
building blocks for boxy and peanut (hereafter b/p) edge-on profiles. We find
cases where the b/p profile is confined to the central parts of the model and
cases where a major fraction of the bar participates in this morphology. A b/p
feature can be built either by 3D families associated with 3D bifurcations of
the x1 family, or, in some models, even by families related with the z-axis
orbits and existing over large energy intervals. The {\sf `X'} feature observed
inside the boxy bulges of several edge-on galaxies can be attributed to the
peaks of successive x1v1 orbits (Skokos et al. 2002a, hereafter paper I),
provided their stability allows it. However in general, the x1v1 family has to
overcome the obstacle of a S\ar\D\ar S transition in order to support the
structure of a b/p feature. Other families that can be the backbones of b/p
features are x1v4 and z3.1s. The morphology and the size of the boxy or
peanut-shaped structures we find in our models is determined by the presence
and stability of the families that support b/p features. The present study
favours the idea that the observed edge-on profiles are the imprints of
families of periodic orbits that can be found in appropriately chosen
Hamiltonian systems, describing the potential of the bar.
