Clogauite, ideally PbBi4Te4S3 is the new n = 1 member of the aleksite series, PbnBi4Te4Sn+2, where n is the homologue number. Clogauite is named from the type locality, the Clogau gold mine, Dolgellau Gold belt, Gwynedd, North Wales, United Kingdom. The mineral and name have been approved by the Commission on New Minerals, Nomenclature and Classification of the International Mineralogical Association (IMA2023–062). The aleksite series is an accretional homologous series in which each member is derived from the same 5-atom tetradymite archetype. Clogauite crystallises in the trigonal crystal system (space group: P$\bar{3}$m1, #164). Three distinct polytypes of clogauite are recognised, corresponding to identical chemistry but different layer sequences, expressed as (57), (5559) and (557.559), respectively, in reference to the number of atoms in individual layer sequences. These are clogauite-12H, a = 4.277(4) Å, c = 23.46(14) Å, V = 371.598 Å3 and Z = 1; clogauite-24H, a = 4.278(4) Å, c = 46.88(31) Å, V = 743.053 Å3 and Z = 2; and clogauite-36H, a = 4.278(4) Å, c = 70.36(32) Å, V = 1115.283 Å3 and Z = 3. Clogauite is opaque, with a pale grey colour in reflected light. Reflectance is higher than tetradymite or galena. Bireflectance and anisotropy are strong. Structural data were determined from measurement of atomic-scale HAADF STEM imaging showing the internal arrangement of component atoms and characteristic selected area electron diffraction patterns for each polytype. The structures were then further constrained from ab initio total energy calculations and structure relaxation using density functional theory (DFT) using the measured parameters as input data. The relaxed crystal structure for each polytype was modelled to generate crystallographic information files (cif). STEM and electron diffraction simulations based on the crystallographic information data obtained from the DFT calculations show an excellent match to the empirical measurements.