Exact quantum dynamics calculations of the eigenstate energy levels and wavefunctions for all bound rovibrational states of the Ne3 trimer (J 0-18) have been performed using the ScalIT suite of parallel codes. These codes employ a combination of highly efficient methods, including phase-space optimized discrete variable representation, optimal separable basis, and preconditioned inexact spectral transform methods, together with an effective massive parallelization scheme. The Ne3 energy levels and wavefunctions were computed using a pair-wise Lennard-Jones potential. Jacobi coordinates were used for the calculations, but to identify just those states belonging to the totally symmetric irreducible representation of the G 12 complete nuclear permutation-inversion group, wavefunctions were plotted in hyperspherical coordinates. Horseshoe states were observed above the isomerization barrier, but the horseshoe localization effect is weaker than in Ar3. The rigid rotor model is found to be applicable for only the ground and first excited vibrational states at low J; fitted rotational constant values are presented.