  The mechanics of epithelial tissues, which is governed by forces generated in
various cell domains, is often investigated using two-dimensional models that
account for the apically-positioned actomyosin structures but neglect
basolateral mechanics. We employ a more detailed three-dimensional model to
study how lateral surface tensions affect the structure and rigidity of such
tissues. We find that cells are apicobasally asymmetric, with one side
appearing more ordered than the other depending on cell target perimeter. In
contrast to the 2D model, which predicts a rigidity transition at large target
perimeters, tissues in the 3D model remain solid-like across all parameter
space.
