High resolution spectroscopic data for H-3(+), H2D+, D2H+, and D-3(+) is used to determine effective, mass-dependent potential energy surfaces for each isotopomers. These surfaces are expressed as a sum of the mass-independent Born-Oppenheimer (BO) potential and a mass dependent adiabatic correction. For H-3(+) and D-3(+) the adiabatic correction is a single surface of the same symmetry and functional form as the BO surface. For H2D+ and D2H+ a second, lower symmetry surface is required. Fits to all three surfaces were started from recent, high quality ab initio calculations. The standard deviations for fits using all the available data with J less than or equal to 9 are 0.015 cm(-1) for H-3(+), 0.010 (-1) for H2D+ and D2H+ combined, and 0.015 cm(-1) for D-3(+). These values are close to the intrinsic experimental error of much of the data and improve on the corresponding ab initio surfaces by at least an order of magnitude. The fits are very compact : nearly 1600 data are fitted by adjusting 36 constants and freezing 51 at their ab initio values.