We model short-period superlattices of WO$_3$ and ReO$_3$ with first-principles calculations. In fully-relaxed superlattices, we observe that octahedral tilts about an axis in the planes of the superlattices do not propagate from one material, despite the presence of the corner-shared oxygen atoms. However, we find that octahedral rotation is enhanced within WO$_3$ layers in cases in which strain couples with native antiferroelectric displacements of tungsten within their octahedral cages. Resulting structures remain antiferroelectric with low net global polarization. Thermodynamic analysis reveals that superlattices with sufficiently thick ReO$_3$ layers, the absolute number being three or more layers and the Re fraction $geq 50%$, tend to be more stable than the separated material phases and also show enhanced octahedral rotations in the WO$_3$ layers.
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