New germanides with composition RE₃Pt₄Ge₁₃ (RE = Y, Pr, Sm, Gd, Tb, Tm) have been prepared by high-pressure, high-temperature synthesis. Their crystal structures have been refined, and the relationship of this new rhombohedral and monoclinic structure types with the primitive cubic Yb₃Rh₄Sn₁₃ prototype is discussed. Band structure calculations within density functional theory confirm the distorted rhombohedral and monoclinic structural arrangements to be energetically more favorable than the simple cubic one. X-ray absorption spectroscopy and magnetic susceptibility measurements indicate that the RE-atoms are in the +3 oxidation state in all studied compounds.