The 1D coordination polymer (CP) [(Me2S)(3){Cu-2(mu-I)(2)}](n) (1) is formed when CuI reacts with SMe2 in n-heptane, whereas in acetonitrile (MeCN), the reaction forms exclusively the 2D CP [(Me2S)(3){Cu-4(mu-I)4}](n) (2) containing flower-basket Cu4I4 units. The reaction product of CuI with MeSEt is also solvent-dependent, where the 1D polymer [(MeSEt)(2){Cu-4(mu(3)-I)(2)(mu(2)-I)(2)}(MeCN)(2)](n) (3) containing stepped-cubane Cu4I4 units is isolated in MeCN. In contrast, the reaction in n-heptane affords the 1D CP [(MeSEt)(3){Cu-4(mu(3)-I)4}](n) (4) containing closed-cubane Cu4I4 clusters. The reaction of MeSPr with CuI provides the structurally related 1D CP [(MeSPr)(3){Cu-4(mu(3)-I)4}](n) (5), for which the X-ray structure has been determined at 115, 155, 195, 235, and 275 K, addressing the evolution of the metric parameters. Similarly to 4 and the previously reported CP [(Et2S)(3){Cu-4(mu(3)-I)4}](n) (Inorg. Chem. 2010, 49, 5834), the 1D chain is built upon closed cubanes Cu-4(mu(3)-I)4 as secondary building units (SBUs) interconnected via mu-MeSPr ligands. The 0D tetranuclear clusters [(L)4{Cu-4(mu(3)-I)4}] [L = EtSPr (6), Pr2S (7)] respectively result from the reaction of CuI with EtSPr and n-Pr2S. With i-Pr2S, the octanuclear cluster [(i-Pr2S)(6){Cu-8(mu(3)-I)(3)}(mu(4)-I)(2)}] (8) is formed. An X-ray study has also been performed at five different temperatures for the 2D polymer [(Cu3Br3)(MeSEt)(3)](n) (9) formed from the reaction between CuBr and MeSEt in heptane. The unprecedented framework of 9 consists of layers with alternating Cu(mu(2)-Br)(2)Cu rhomboids, which are connected through two mu-MeSEt ligands to tetranuclear open-cubane Cu4Br4 SBUs. MeSPr forms with CuBr in heptane the 1D CP [(Cu3Br3)(MeSPr)(3)](n) (10), which is converted to a 2D metalorganic framework [(Cu5Br5)(mu(2)-MeSPr)(3)](n) (11) incorporating pentanuclear [(Cu-5(mu(4)-Br)(mu(2)-Br)] SBUs when recrystallized in MeCN. The thermal stability and photophysical properties of these materials are also reported.