The crystal structure of the late lanthanoids' catena-polyphosphates Ln(PO3)(3) (Ln = Tb-Yb) is incommensurately modulated (Dy(PO3)(3): space group Cc(0 beta 0)0; Z = 4; a = 1417.4(4), b = 670.96(14), c = 1009.5(3) pm; beta = 127.62(2)degrees, q= 0.364b*; R-all = 0.057, wR(all) = 0.071; 293 K) and consists of infinite chains of corner-sharing PO4 tetrahedra. The cations are coordinated 6-fold in an almost octahedral arrangement over the whole modulation period. All atoms comprise a sinoidal positional modulation. The basic structure can be derived from a fcc packing which explains the pseudo-face-centering observed in the diffraction patterns. The crystal structure of Lu(PO3)(3) is isotypic with C-type phosphates (Cc; Z = 12; a = 1397.2(1), b = 2001.8(2), c = 995.56(9) pm; beta = 127.351(6)degrees; R1 = 0.042, wR2 = 0.097, 293 K), and Gd(PO3)(3) crystallizes in a new structure type (I2/a; Z = 16; a = 2601.7(2), b = 1351.1(1), c = 1008.4(1) pm; beta = 119.311(6)degrees; R1 = 0.039, wR2 = 0.092; 293 K). Both can be described in terms of superstructures of the basic structure unit cell of the incommensurate phases, and thus, a consistent structural description of many polyphosphates is provided. Tb(PO3)(3) was obtained as single phase adopting a novel synthesis under reducing conditions. The absence of an inversion center in the incommensurate phases and Lu(PO3)(3) was proved by a SHG experiment. The vibrational spectra are also discussed.