Single crystals of ternary borides RRh3B2 (R = Gd, Er, Tm) were successfully grown by the flux method using molten copper as a solvent. Structural properties of the compounds were investigated by X-ray single crystal photography and powder diffraction techniques. A new type of superstructure, with three and six doublings of the reported a-and c-axes, was revealed to exist in all these three borides consisting of different rare earth elements.