  Lattice relaxation in twistronic bilayers with close lattice parameters and
almost perfect crystallographic alignment of the layers results in the
transformation of moir\'e pattern into a sequence of preferential stacking
domains and domain wall networks. Here, we show that reconstructed moir\'e
superlattices of the perfectly aligned heterobilayers of same-chalcogen
transition metal dichalcogenides have broken-symmetry structures featuring
twisted nodes ('twirls') of domain wall networks. Analysing
twist-angle-dependences of strain characteristics for the broken-symmetry
structures we show that the formation of twirl reduces amount of hydrostatic
strain around the nodes, potentially, reducing their infuence on the band edge
energies of electrons and holes.
