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We used high-angle annular dark field scanning transmission electron microscopy (HAADF STEM) to image the crystal structures of four minerals in the Bi₄X₃ isoseries (X = Te, Se, S), a subgroup of the tetradymite homologous series: ikunolite (Bi₄S₃), laitakarite (Bi₄Se₂S), joséite-B (Bi₄Te₂S), and joséite-A (Bi₄TeS₂). The four minerals are isostructural and interpretable in terms of regular stacking of seven-atom packages: [Bi–S–Bi–S–Bi–S–Bi], [Bi–Se–Bi–S–Bi–Se–Bi], [Bi–Te–Bi–S–Bi–Te–Bi], and [Bi–S–Bi–Te–Bi–S–Bi], respectively. The four phases are mixed-layer structures representing the Bi_2kTe₃ (k = 2) module within the tetradymite series. Diffraction patterns confirm they are seven-fold superstructures of a rhombohedral subcell with <i>c</i>/3 = d~1.89–1.93 Å. Modulation along the d* interval matches calculations of reflection intensity using the fractional shift method for Bi₄X₃. Internal structures can be discerned by high-resolution HAADF STEM imaging and mapping. Paired bismuth atoms are positioned at the outside of each seven-atom layer, giving the minerals a modular structure that can also be considered as being composed of five-atom (X–Bi–X–Bi–X) and two-atom (Bi–Bi) sub-modules. The presence of mixed sites for substituting cations is shown, particularly for Pb. Moreover, Pb may be important in understanding the incorporation of Ag and Au in Bi–chalcogenides. Visualisation of crystal structures by HAADF STEM contributes to understanding relationships between phases in the tetradymite homologous series and will play an invaluable role in the characterization of potential additional members of the series.