First direct identification of the barlens vertical structure in galaxy
  models
  Applying spectral dynamics methods to one typical $N$-body model with a
barlens, we dissect the modelled bar into separate components supported by
completely different types of orbits. We identify at least four components: a
narrow elongated bar, a boxy bar, and two components contributing to the
barlens. We analyse the vertical structure of all components that make up the
thick part of the bar, which has a boxy/peanut shape (B/P bulge). We show that
the `peanut' shape is mainly due to the orbits that assemble the boxy part of
the face-on bar. We associate the X-shape with the narrow and elongated bar.
The wider part of the barlens with square-like isophotes contributes to the
boxy shape of the B/P bulge when we observe the galaxy edge-on. However, the
part of the barlens with rounded isophotes in the face-on view is a rather flat
structure in the vertical direction without any significant off-centre
protrusions. Thus, for the first time, we demonstrate that the rounded face-on
barlens cannot be entirely associated with the B/P bulge.
