The new synthetic phase, ~Sn12In19(Se,S)41, synthesized in the condensed system Fe–Sn–Sb–In–S–Se at 600°C, is monoclinic with a 56.29(4), b 3.924(3), c15.916(10) Å, β 102.56(1)°, space group C2/m, and Z = 2. It occurs as needle-like crystals together with chemically analyzed Fe9S10, FeIn2(S,Se)4, ~SbSn9(Se,S)10 and ~Sn4Sb3In2(S,Se)11. The crystal structure has been refined to a conventional R factor R1 of 6.29% for 2339 unique reflections with Fo>4σ(Fo). There are 16 unique sites of Sn and In and 21 unique sites of (Se,S) in the asymmetric unit. It is a composite-layer structure with two kinds of layers in regular alternation; together, they undergo a step-like modulation. The pseudotetragonal layers are three atomic planes thick and modified by steps into oval-shaped fragments containing octahedra of indium and trigonal coordination prisms of tin. Single-octahedron pseudohexagonal layers are of two regularly alternating kinds: those with an overlap of two octahedra in the step region and those with a gap of one octahedron in those regions. The title compound, ~Sn12In19(Se,S)41, is a member of a M15+NS20+N series of closely related composite-layer structures with alternating, periodically sheared pseudohexagonal and pseudotetragonal layers (a “sliding series” according to its main structural principle of slabs with fixed step-like configurations sliding past one another and thus creating chemical and structural differences on the planes of their contact). A parallel series with less frequently sheared layers is known only from the Pb6In13.34S26 – Sn5In14S26 pair. Two cannizzarite-related structures with layers unsheared, one potential cylindrite-type structure, two families of rod-based structures, one known complex sulfide with In–In bonds, and the structure of PbIn2S4 are further principal structure-types of complex indium sulfides in addition to members of the pavonite homologous series and several individual sulfosalt structures that are in need of revision. Alternation of pseudotetragonal and pseudohexagonal layers and formation of rod-based structures are the two basic principles in the construction of complex sulfides and selenides of indium.