Four new one-dimensional tellurides have been synthesized and structurally characterized by single-crystal X-ray diffraction. The reaction of K4SnTe4 with HgCl2 in a 1:1 molar ratio in ethylenediamine (en) at 100-degrees-C for 2 days, in a sealed evacuated quartz ampule, gives a nearly quantitative yield of the novel one-dimensional (1-D) telluride polymer K2HgSnTe4 (1). Black cubic-shaped crystals of 1 crystallize in the tetragonal space group I4/mcm (No. 140) with a = 8.580(2) and c = 7.358(4) angstrom, V = 541.6(4) angstrom3, Z = 4, and R(R(w)) = 0.046(0.047). The en extraction of an alloy of the composition K2HgSnTe4 followed by treatment with Et4NI gives (Et4N)2[HgSnTe4] (2) in 30% yield. Telluride 2 crystallizes in the tetragonal space group P4(2)/mnm (No. 136) with a = 14.614(2) and c = 7.585(1) angstrom, V = 1619.9(4) angstrom3, Z = 4, and R(R(w)) = 0.040(0.053). The reaction of K4Ge4Te10 with InCl3 in the presence of Ph4PBr in ethylenediamine (en) at 100-degrees-C for 3 days, in a sealed evacuated quartz ampule, affords a new (1-D) telluride polymer (Ph4P)[GeInTe4] (3) in 68% yield. Black tetragonal plate crystals of (3) crystallize in the tetragonal space group P4(2)/n (No. 86) with a = 14.2770(8) and c = 7.029(1) angstrom, V = 1432.8(2) angstrom3, Z = 2 and R(R(w)) = 0.071(0.086). The high-temperature reaction of Rb2Te2, In, and Te at 400-degrees-C, in a sealed evacuated quartz tube for 24 h followed by slow cooling gives the one-dimensional polymer RbInTe2 (4) in 64% yield. Red needle crystals of 4 crystallize in the tetragonal space group I4/mcm (No. 140) with a = 8.8168(6) and c = 7.376(1) angstrom, V = 573.3(1) angstrom3, Z = 4, and R(R(w)) = 0.034(0.042). Single crystal X-ray diffraction studies revealed that the four structures have similar anions and consist of 1-D chains of edge-sharing tetrahedra with metal atoms at the center of each tetrahedron. The chains in telluride 1 and 4 crystallize such that the Te atoms are close packed with the alkali-metal cations occupying interchain 1-D tunnels that run parallel to [001], whereas in 2 and 3 the chains are well separated by the organic cations. Diffuse scans along the c axis for 1 and 2 show no evidence of superstructures, indicating that the Hg and Sn form a solid solution in both structures. The 1-D chains of [GeInTe4]- in telluride 3 have the Ge4+ and In3+ atoms situated on two crystallographically independent sites. Powder X-ray diffraction measurements indicate that it is also possible to prepare K2HgSnTe4 (1) from K2Te, Sn, Hg, and Te at 500-degrees-C.