Structures of tripotassium tetrasodium dihydrogen decatungstolanthanoate crystals, K3Na4H2[LnW10O36].-nH2O (Ln = Pr, Nd, Dy; n = 21-22), have been determined and compared with the structures of their isomorphous crystals with Ln = Sm, Gd and Tb. K3Na4H2[PrW10O36].22H2O crystallizes in monoclinic, P2(1)/n, a = 30.049 (4), b = 16.055 (2), c = 11.462 (2) angstrom, beta = 96.36 (1)-degree, V = 5496 (1) angstrom3 and R = 0.056 for 7990 reflections. K3Na4H2[NdW10O36].22H2O crystallizes in monoclinic, P2(1)/n, a = 30.057 (5), b = 16.051 (4), c = 11.468 (2) angstrom, beta = 96.52 (2)-degree, V = 5497 (2) angstrom3 and R = 0.052 for 6432 reflections. K3Na4H2[DyW10O36].21H2O crystallizes in monoclinic, P2(1)/n, a = 29.816 (6), b = 16.097 (4), c = 11.443 (2) angstrom, beta = 96.36 (2)-degrees, V = 5458 (2) angstrom3 and R = 0.053 for 6114 reflections. All six [LnW10O36]9- anions in these isomorphous crystals exhibit structural distortion from their ideal symmetry of D4d in a way that the diheral twofold symmetry is lost, which is most evident in that Ln-W distances are about 0.04 angstrom longer in one [W5O18]6- group than in the other. This distortion originates in the coordination of the K+ cations to the O atoms of the central LnO8 square antiprisms in the [LnW10O36]9- anions. The Ln-O distances in the six decatungstolanthanoate anions correlate with the ionic radii of the central lanthanide elements. Average Ln-O distances range from 2.48 angstrom in [PrW10O36]9- to 2.39 angstrom in [DyW10O36]9-, accompanied with the variation in the Ln-W distances from 3.899 to 3.843 angstrom for one [W5O18]6- group and from 3.849 to 3.807 angstrom for the other group.