  An exact solution (incomplete) of the ground-state problem for an Ising model
in an external field on a 3D honeycomb zigzag-ladder lattice with two types of
sites is found. It is shown that the geometrical frustration due to the
presence of triangle elements leads to the emergence of a variety of magnetic
phases. The majority of these are partially disordered (highly degenerate). The
theoretical results are used to explain the sequence of experimentally observed
phase transitions in the honeycomb zigzag-ladder magnets and to predict the
appearance of new phases.
