  The topic of this contribution is the investigation of quantum states and
quantum Hall effect in electron gas subjected to a periodic potential of the
lateral lattice. The potential is formed by triangular quantum antidos located
on the sites of the square lattice. In a such system the inversion center and
the four-fold rotation symmetry are absent. The topological invariants which
characterize different magnetic subbands and their Hall conductances are
calculated. It is shown that the details of the antidot geometry are crucial
for the Hall conductance quantization rule. The critical values of lattice
parameters defining the shape of triangular antidots at which the Hall
conductance is changed drastically are determined. We demonstrate that the
quantum states and Hall conductance quantization law for the triangular antidot
lattice differ from the case of the square lattice with cylindrical antidots.
As an example, the Hall conductances of magnetic subbands for different antidot
geometries are calculated for the case when the number of magnetic flux quanta
per unit cell is equal to three.
