A coupled three-dimensional model calculation of the low-frequency large-amplitude intermolecular torsional states in (H₂O)₃ and (D₂O)₃ is presented, based on the analytical modEPEN intermolecular potential surface and a three-dimensional discrete variable representation approach. The lowest torsional levels of both (H₂O)₃ and (D₂O)₃ lie above the sixfold (upd) torsional barrier. The first eight (eleven) torsions of (H₂O)₃ ((D₂O)₃) are pseudorotational states. The ‘radial’ and ‘polar’ torsional fundamental frequencies are predicted at 151 and 160 cm^−1 for (D₂O)₃, and for (H₂O)₃ at 185.0 and 185.3 cm^−1, respectively. Each of these in turn support a ladder of pseudorotational levels.