Topological insulators (TIs) are semiconductors with protected electronic surface states that allow dissipation-free transport. TIs are envisioned as ideal materials for spintronics and quantum computing. In Bi14Rh3I9, the first weak 3D TI, topology presumably arises from stacking of the intermetallic [(Bi4Rh)3I]2þ layers, which are predicted to be 2D TIs and to possess protected edge-states, separated by topologically trivial [Bi2I8]2+ octahedra chains. In the new layered salt Bi12Rh3Cu2I5, the same intermetallic layers are separated by planar, i.e., only one atom thick, [Cu2I4]2- anions. Density functional theory (DFT)-based calculations show that the compound is a weak 3D TI, characterized by Z2 ¼ ð0; 0001Þ, and that the topological gap is generated by strong spin–orbit coupling (Eg,calc.~ 10 meV). According to a bonding analysis, the copper cations prevent strong coupling between the TI layers. The calculated surface spectral function for a finite-slab geometry shows distinct characteristics for the two terminations of the main crystal faces 〈001〉, viz., [(Bi4Rh)3I]2þ and [Cu2I4]2-. Photoelectron spectroscopy data confirm the calculated band structure. In situ four-point probe measurements indicate a highly anisotropic bulk semiconductor (Eg,exp.¼ 28 meV) with pathindependent metallic conductivity restricted to the surface as well as temperatureindependent conductivity below 60 K.