  We study the dynamical mechanisms that reinforce the formation of boxy
structures in the \textit{inner} regions, roughly in the middle, of bars
observed nearly \textit{face-on}. Outer boxiness, at the ends of the bars, is
usually associated with orbits at the inner, radial 4:1 resonance region and
can be studied with 2D dynamics. However, in the middle of the bar dominate 3D
orbits that give boxy/peanut bulges in the edge-on views of the models. In the
present paper we show that 3D quasi-periodic, as well as 3D chaotic orbits
sticky to the x1v1 and x1v1$^{\prime}$ tori, especially from the Inner Lindblad
Resonance (ILR) region, have boxy projections on the equatorial plane of the
bar. The majority of vertically perturbed 2D orbits, initially on the
equatorial plane in the ILR resonance region, enhance boxy features in face-on
bars. Orbits that build a bar by supporting sharp "{\sf X}" features in their
side-on views at energies \textit{beyond} the ILR, may also have a double boxy
character. If populated, the extent of the inner boxiness along the major axis
is about the same with that of the peanut supporting orbits in the side-on
views. At any rate these orbits do not obscure the observation of the boxy
orbits of the ILR region in the face-on views, as they contribute more to the
surface density at the sides of the bar than to their central parts.
