In the search for new magnetic topological insulators with strong spin-orbit coupling, by following conceptual considerations that have already proven to be suitable, the bismuth-rich subiodide Mn[PtBi₆I₁₂] was discovered. Single crystals were grown from mixtures of the elements and BiI₃ using a temperature program developed on the basis of thermal analyses. Single-crystal X-ray diffraction revealed a rhombohedral structure of the cuboctahedral cluster anions [PtBi₆I₁₂]^2-, which are linked into chains via octahedrally coordinated Mn²⁺ cations. Partial substitution of Mn²⁺ by Bi³⁺ and vacancy formation are responsible for a phase width represented by the general formula (Mn_1-3xBi_2x)[PtBi₆I₁₂]. Density functional theory-based calculations and measurements of the electrical resistance showed that the compound is a semiconductor with a topologically trivial band gap. Nonstoichiometry of chain fragments, corresponding to n- and p-self-doping, strongly increases the conductivity, especially along the chains. The compound is paramagnetic at room temperature. Electron spin resonance spectra indicate an increase in spin correlations and the buildup of internal fields below 30 K.