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Crystals of RETe1.875±δ (RE = Ce, Pr, Sm, Gd; 0.004 ≤ δ ≤ 0.025) were grown using alkali halide flux and chemical transport reactions. The crystal structures are described in space group Amm2 (no. 38), with lattice parameters of a = 13.3729(5) Å, b = 17.7918(5) Å, c = 18.1561(4) Å for CeTe1.87(1) (T = 100 K), a = 13.271(2) Å, b = 17.747(3) Å, c = 18.160(3) Å for PrTe1.85(1) (T = 100 K), a = 13.1251(6) Å, b = 17.4269(8) Å, c = 17.8808(8) Å for SmTe1.87(1) (T = 100 K), and a = 13.1762(4) Å, b = 17.4995(5) Å, c = 17.9591(5) Å for GdTe1.88(