  We provide a brane realization of 2d (0,2) Gadde-Gukov-Putrov triality in
terms of brane brick models. These are Type IIA brane configurations that are
T-dual to D1-branes over singular toric Calabi-Yau 4-folds. Triality translates
into a local transformation of brane brick models, whose simplest
representative is a cube move. We present explicit examples and construct their
triality networks. We also argue that the classical mesonic moduli space of
brane brick model theories, which corresponds to the probed Calabi-Yau 4-fold,
is invariant under triality. Finally, we discuss triality in terms of phase
boundaries, which play a central role in connecting Calabi-Yau 4-folds to brane
brick models.
