= Solution
The square-planar rotor is an <oblate symmetric top>. A parallel band has $\Delta K=0$ and $\Delta J=0,\pm1$, producing P and R progressions with approximate spacing $2\widetilde B$ and a central Q contribution from $K\ne0$; the $K=0$ parallel Q branch is absent. At modest resolution many nearly coincident $K$ components merge.
A perpendicular band has $\Delta K=\pm1$ and $\Delta J=0,\pm1$. Its Q subbranches produce a characteristic series of sharper features on the broader unresolved P/R envelope. Neglecting changes of rotational constants on vibration, successive perpendicular Q features are separated by approximately $2|\widetilde B-\widetilde C|$. These are rotational contours rather than extra normal-mode fundamentals.
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