The new mineral tombstoneite (IMA2021-053), (Ca0.5Pb0.5)Pb3Cu2+6Te6+2O6(Te4+O3)6(Se4+O3)2(SO4)2⋅3H2O, occurs at the Grand Central mine in the Tombstone district, Cochise County, Arizona, USA, in cavities in quartz matrix in association with jarosite and rodalquilarite. Tombstoneite crystals are green pseudohexagonal tablets, up to 100 μm across and 20 μm thick. The mineral has a pale green streak and adamantine lustre. It is brittle with irregular fracture and a Mohs hardness of ~2½. It has one perfect cleavage on {001}. The calculated density is 5.680 g cm–3. Optically, the mineral is uniaxial (–) and exhibits pleochroism: O = green, E = light yellow green; O > E. The Raman spectrum exhibits bands consistent with Te6+O6, Te4+O3, Se4+O3 and SO4. Electron microprobe analysis provided the empirical formula (Ca0.51Pb0.49)Σ1.00Pb3.00Cu2+5.85Te6+2.00O6(Te4+1.00O3)6(Se4+0.69Te4+0.24S0.07O3)2(S1.00O4)2⋅3H2O. Tombstoneite is trigonal, P321, a = 9.1377(9), c = 12.2797(9) Å, V = 887.96(18) Å3 and Z = 1. The structure of tombstoneite (R1 = 0.0432 for 1205 I > 2σI) contains thick heteropolyhedral layers comprising Te6+O6 octahedra, Jahn-Teller distorted Cu2+O5 pyramids, Te4+O3 pyramids and Se4+O3 pyramids. Pb2+ cations without stereoactive 6s2 lone-pair electrons are hosted in pockets in the heteropolyhedral layer. Pb2+ cations, possibly with stereoactive 6s2 lone-pair electrons, are located in the interlayer region along with SO4 tetrahedra and H2O groups. Within the heteropolyhedral layer, the Te6+O6 octahedra and the Te4+O3 pyramids form finite Te6+O3(Te4+O3)3 clusters with a pinwheel-like configuration. This is the first known finite complex including both Te4+ and Te6+ polyhedra in any natural or synthetic tellurium oxysalt structure.