  By means of the operator extension theory, we construct an explicitly
solvable model of a simple-cubic three-dimensional regimented array of quantum
dots in the presence of a uniform magnetic field. The spectral properties of
the model are studied. It is proved that for each magnetic flux the band is the
image of the spectrum of the tight-binding operator under an analytical
transformation. In the case of rational magnetic flux the spectrum is described
analytically. The flux-energy and angle-energy diagrams are obtained
numerically.
