Microwave rotational spectra of eleven isotopomers of the Ne-3-NH3 van der Waals tetramer were measured using a pulsed jet, Balle-Flygare type Fourier transform microwave spectrometer. The transitions measured fall between 4 and 17 GHz and correspond to the ground internal rotor state of the weakly bound complex. The Ne-20(3)- and Ne-22(3)-Containing species are symmetric top molecules while the mixed (Ne2Ne)-Ne-20-Ne-22- and (NeNe2)-Ne-20-Ne-22-isotopomers are asymmetric tops. For each of the deuterium-containing isotopomers, a tunneling splitting was observed due to the inversion of NH3 within the tetramer. The N-14 nuclear quadrupole hyperfine structures were resolved and included in the spectroscopic fits of the various isotopomers. The rotational constants obtained from the fits were used to estimate the van der Waals bond lengths of the tetramer while the N-14 nuclear quadrupole coupling contants and the observed inversion tunneling splittings provided information about the internal dynamics of the NH3 moiety. The experimental results were complemented by the construction of three ab initio potential energy surfaces [CCSD(T)] for the Ne-3-NH3 complex, each corresponding to a different internal geometry of NH3 (