  Duality cascades are a series of duality transformations in field theories,
which can be realized as the Hanany-Witten transitions in brane configurations
on a circle. In the setup of the ABJM theory and its generalizations, from the
physical requirement that duality cascades always end and the final destination
depends only on the initial brane configuration, we propose that the
fundamental domain of supersymmetric brane configurations in duality cascades
can tile the whole parameter space of relative ranks by translations, hence is
a parallelotope. We provide our arguments for the proposal.
