Three new copper iodobismuthates, red tetranuclear [n-Bu4N][Cu-2(CH3CN)(2)Bi2I10] (1), dark-red infinite linear [Et4N](2n)[Cu2Bi2I10](n) (2), and black polymeric ladderlike [Cu(CH3CN)(4)](2n)[Cu2Bi2I10]n (3), crystallize from solutions of BiI3 and CuI in the presence of different cations. A regular structural relationship from 0-D (1) to 1-D linear anion chains (2) to 1-D ladderlike anion chains (3) is observed. The self-assembly of the basic building unit Cu2Bi2I10 as altered by different cations is proposed to be the driving force for their formation. The optical band gaps exhibit a structure-related decrease from 1 to 2/3, in agreement with their color changes and the density functional theory (DFT) calculation results. The electronic structures and the relationship with corresponding monobismuth analogues and the Ag-Bi isotypes are discussed on the basis of DFT calculations. In spite of their structural similarities, the compounds are distinctive thermally: 2 is stable to 230 degrees C, 1 undergoes a solvent loss at 85 degrees C to form a new phase that is thermally stable to 230 degrees C, and 3 releases a solvent molecule and decomposes at 80 degrees C into BiI3 and CuI. The essential reasons for these differences are discussed.