Large basis set ab initio calculations have been carried out for a dense grid of points on the He-3 potential energy surface. Three-body contributions were extracted at every point, and a number of concise functional representations for the three-body potential surface were then examined. Three-body multipolar dispersion terms and other radial and angular terms were used in the representations, and an assessment of relative importance of the different terms is presented. Combined with a two-body He-He potential, the results of this work should offer a high quality interaction potential for simulations of aggregated helium.