Black needle-shaped crystals of the bismuth-rich mixed halogenide Bi₂₁Rh₄Cl₆I₇ were obtained by slow cooling of a melt of Bi, RhI₃ and BiCl₃. Single-crystal X-ray diffraction revealed an orthorhombic structure that consists of infinite intermetallic rods (Figure presented.) Bi₉Rh₂]³⁺ and discrete anionic groups [Bi^II₂Cl₂I₅]³⁻ and [Bi^IIICl₄I₂]³⁻. The rods consist of Rh-centered [RhBi₈] polyhedra that alternately share triangular and rectangular faces. Using traditional electron counting rules, the rod can be interpreted as a covalent polymer with Rh₂ dumbbells bonded to molecular Bi₂ and Bi₅ units. However, a quantum-chemical bonding analysis shows that the bonds involving Rh atoms are largely diffuse, while two-center bonds dominate in the bismuth units. The below 240 K observed semiconducting behavior of Bi₂₁Rh₄Cl₆I₇ is consistent with a complete localization of the valence electrons. Above 240 K, the resistance along the needle axis is largely independent of temperature.