Bi₁₂Rh₃Br₂ was synthesized from the elements using niobium bromides as auxiliaries to modify the partial pressures in the course of the reaction. The orthorhombic crystal structure (space group Fddd (no. 70); a = 717.12(3) pm, b = 1680.37(6) pm, c = 3187.1(1) pm) consists of a three-dimensional framework of [RhBi₈] cubes and square antiprisms, which share common edges. Bromide ions fill the chiral pores of the framework. The crystal structure of Bi₁₂Rh₃Br₂ = (Bi₄Rh)₃Br₂ is closely related to that of the intermetallic compound α-Bi₄Rh. The oxidation of Bi₄Rh to Bi₁₂Rh₃Br₂ is accompanied by an emptying of Bi-Bi and Bi-Rh antibonding states near the Fermi level, leading to a strengthening of bonding in the intermetallic part of the structure. Despite the partial oxidation the metallic conductivity is retained.