Hexanuclear chalcohalide clusters of rhenium(III) of general formula [Re6S4+xCl10-x](x-) with x = 1-4 have been studied using quantum chemical DFT calculations, The optimized structures reproduce the geometrical features found from X-ray data for the members of the series. The relative stability of different stereoisomers for the mono- and dianions has been estimated. The analysis of the tetraanion series [Re(6)Q(8)X(6)](4-) with Q = S, Se and X = Cl, Br, 1, and CN demonstrates the influence of the mu(1)- and mu(3)-ligands on the strength of Re-apical ligand bond. It is shown that the tetragonal distortion found for the stable oxidized paramagnetic species [Re6S8Cl6](.3-) results from the Jahn-Teller effect for a doubly degenerate electronic state.