Crystals of Bi₃Ni were synthesized using iodine as mineralizer. X-ray diffraction on a single-crystal including transmission-optimized measurement and optimized absorption correction (μ(Mo-K_α) = 1302 cm^-1) results in a structure model (Pnma; a = 887.96(7), b = 409.97(3), c = 1147.8(1) pm) with significant deviations in interatomic distances compared with previous data from X-ray and neutron investigations. From quantum chemical calculations and from the structural chemistry of the subhalides related to Bi₃Ni the chemical structure of the intermetallic compound can be derived. In the crystal structure the Ni atoms have a capped trigonal prismatic coordination of Bi atoms with strong bonds Ni-Bi and Ni-Ni. The prisms constitute rods _∞¹ [NiBi_1/1Bi_6/3] by sharing the non-capped square faces. The bonding between the intermetallic rods is clearly weaker than inside them, leading to a preservation of this structural fragment in the subhalides of Bi₃Ni. In accordance with the low temperature superconductivity of the compound, its electronic band structure shows steep and flat bands at the Fermi level. DFT and ELF calculations reveal a separation of delocalized conduction electrons inside the prism rods and largely localized valence electrons between them.