Abstract: There are diverse crystalline materials where low-energy excitations of the lattice are described by Dirac-type equation with pseudo-spin-one. The spectrum of these systems consists of three energy bands, where two of them give rise to the Dirac cones while the third one can represent the flat-band. It will be shown in the talk that supersymmetric transformations can be used effectively for construction of such systems with tunable values of the flat band. We will consider construction of one-dimensional crystals based on Su-Schriefer-Heeger (SSH) model. We will show that the susy transformation can decorate locally the SSH ladder by an additional chain of atoms.