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The crystal structure of tlapallite has been determined using single-crystal X-ray diffraction and supported by electron probe micro-analysis, powder diffraction and Raman spectroscopy. Tlapallite is trigonal, space group P321, with a = 9.1219(17) Å, c = 11.9320(9) Å and V = 859.8(3) Å3, and was refined to R_1 = 0.0296 for 786 reflections with I > 2σ(I). This study resulted from the discovery of well-crystallised tlapallite at the Wildcat prospect, Utah, USA. The chemical formula of tlapallite has been revised to (Ca,Pb)_3CaCu_6[Te^(4+)_3Te^(6+)O_(12)]_2(Te^(4+)O_3)_2(SO_4)_2·3H_2O, or more simply (Ca,Pb)_3CaCu_6Te^(4+)_8Te^(6+)_2O_(30)(SO_4)_2·3H_2O, from H_6(Ca,Pb)_2(Cu,Zn)_3(TeO_3)_4(TeO_6)(SO_4). The tlapallite structure consists of layers containing distorted Cu^(2+)O_6 octahedra, Te^(6+)O_6 octahedra and Te^(4+)O_4 disphenoids (which together form the new mixed-valence phyllotellurate anion [Te^(4+)_3Te^(6+)O_(12)]^(12−)), Te^(4+)O_3 trigonal pyramids and CaO_8 polyhedra. SO_4 tetrahedra, Ca(H_2O)_3O_6 polyhedra and H_2O groups fill the space between the layers. Tlapallite is only the second naturally occurring compound containing tellurium in both the 4^+ and 6^+ oxidation states with a known crystal structure, the other being carlfriesite, CaTe^(4+)_2Te^(6+)O_8. Carlfriesite is the predominant secondary tellurium mineral at the Wildcat prospect. We also present an updated structure for carlfriesite, which has been refined to R_1 = 0.0230 for 874 reflections with I > 2σ(I). This updated structural refinement improves upon the one reported previously by refining all atoms anisotropically and presenting models of bond valence and Te^(4+) secondary bonding.