The crystal structure of the late lanthanoids' catena-polyphosphates Ln(PO3)3 (Ln=Tb-Yb) is incommensurately modulated (Dy(PO3)3: space group Cc(0beta0)0; Z=4; a=1417.4(4), b=670.96(14), c=1009.5(3) pm; beta=127.62(2) degrees, q=0.364b*; Rall=0.057, wRall=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.