  Epitaxial perovskite oxide interfaces with different symmetry of the
epitaxial layers have attracted considerable attention due to the emergence of
novel behaviors and phenomena. In this paper, we show by aberration corrected
transmission electron microscopy that orthorhombic $\text{LaInO}_\text{3}$
films grow in form of three different types of domains on the cubic
$\text{BaSnO}_\text{3}$ pseudosubstrate. Quantitative evaluation of our TEM
data shows that $c_{pc}$-oriented and $a_{pc}/b_{pc}$-oriented domains are
present with similar probability. While continuum elasticity theory suggests
that $c_{pc}$-oriented domains should exhibit a significantly higher strain
energy density than $a_{pc}/b_{pc}$-oriented domains, density functional
calculations confirm that $c_{pc}$- and $a_{pc}$-oriented domains on
$\text{BaSnO}_\text{3}$ have similar energies.
