  The superlattice of alternating graphene/h-BN few-layered heterostructures is
found to exhibit strong dependence on the parity of the number of layers within
the stack. Odd-parity systems show a unique flamingo-like pattern, whereas
their even-parity counterparts exhibit regular hexagonal or rectangular
superlattices. When the alternating stack consists of seven layers or more, the
flamingo pattern becomes favorable, regardless of parity. Notably, the
out-of-plane corrugation of the system strongly depends on the shape of the
superstructure resulting in significant parity dependence of its mechanical
properties. The predicted phenomenon originates in an intricate competition
between moir\'e patterns developing at the interface of consecutive layers.
This mechanism is of general nature and is expected to occur in other
alternating stacks of closely matched rigid layered materials as demonstrated
for homogeneous alternating junctions of twisted graphene and h-BN. Our
findings thus allow for the rational design of mechanomutable metamaterials
based on Van der Waals heterostructures.
