(i.e., three pairs of cat-like states), forming a benzene-like structure (Fig. \[wigSymAll\](c)). Sub-Planck structures also appear here in the center due to the superposition of three interference regions. A visual analysis shows that the dimension of the sub-Planck scale “tiles” of the compass-like state (Fig. \[wigSymAll\](b)) is smaller than that of the benzene-like state (Fig. \[wigSymAll\](c)). The reason behind it is that the area of overlap increases with the number of split CSs, but we will perform a more quantitative study in the following subsection.

Asymmetric case
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We now discuss sub-Planck scale structures for a strongly asymmetric potential. The potential parameter values are taken as $\rho=50$, $\kappa=6$ and $\alpha=2\;a.u.$, as in Fig. \[potential\] (dashed line). For the sake of comparison with the symmetric case, we choose the CS parameter ($\beta=0.88$), such that the energy distribution is again peaked around $\bar{n}=12$, as in the symmetric case. In spite of this, the interference structures are now very different. The features of the case with large asymmetry is illustrated in Fig. \[wigAsym\]. The cat-like, compass-like, and the benzene-like states become asymmetric and inclined towards the left boundary of the well. Since the potential well is of infinite depth, the stiffness of the 