The metal-rich compound Bi4RhI2 was discovered in a thorough investigation of the Bi-Rh-I phase system. The monoclinic crystal structure was solved via single-crystal X-ray diffraction. It consists of infinite strands of face-sharing distorted square antiprisms (1)(infinity)[RhBi8/2](2+), which are separated by iodide ions. Bi4RhI2 is the high-temperature phase related to the weak three-dimensional topological insulator Bi14Rh3I9 (Bi(46)7Rh(13)) and forms peritectically at 441 degrees C, where Bi14Rh3I9 decomposes. The structure of Bi4RhI2 is compared with Bi4RuI2 and Bi9Rh2I3, all three sharing a similar intermetallic strand-like structure, although their overall count of valence electrons differs. A chemical bonding analysis of Bi4RhI2 via the electron localizability indicator reveals a complex bonding pattern with covalent bonds between rhodium and bismuth, as well as between bismuth atoms and suggests a possible explanation for the formation of this structure type. Band structure calculations indicate a narrow band gap of 157 meV, which was verified by resistivity measurements on a pressed powder pellet and on single crystals. In a broader context, this strandlike structure type accounts for unusual physical phenomena, such as the transition into a charge-density-wave phase.