Orbital Ingredients for Cooking X-structures in Edge-on Galaxies

X-structures are often observed in galaxies hosting the so-called B/PS (boxy/peanuts) bulges and are visible from the edge-on view. They are the most notable features of B/PS bulges and appear as four rays protruding from the disk of the host galaxy and distinguishable against the B/PS bulge background. In some works their origin is thought to be connected with the so-called banana-shaped orbits with a vertical resonance 2:1. A star in such an orbit performs two oscillations in the vertical direction per one revolution in the bar frame. Several recent studies that analyzed ensembles of orbits arising in different $N$-body models do not confirm the dominance of the resonant 2:1 orbits in X-structures. In our work we analyze two $N$-body models and show how the X-structure in our models is gradually assembled from the center to the periphery from orbits with less than 2:1 frequency ratio. The most number of such orbits is enclosed in a 'farfalle'-shape (Italian pasta) form and turns out to be non-periodic. We conclude that the X-structure is only the envelope of regions of high density caused by the crossing or folding of different types of orbits at their highest points, and does not have a "backbone" similar to that of the in-plane bar. Comparing the orbital structure of two different numerical models, we show that the dominance of one or another family of orbits with a certain ratio of the vertical oscillations frequency to the in-plane frequency depends on the parameters of the underlying galaxy and ultimately determines the morphology of the X-structure and the opening angle of its rays.