Investigations in the ternary RE-Mn-Bi systems where RE is an early rare earth element have revealed the existence of the polybismuthides RE3MnBi5 (RE = La-Nd), previously known only for the Ce member, and the new compound Sm2Mn3Bi6. Their structures were determined from single-crystal X-ray diffraction data. The RE3MnBi5 compounds adopt the hexagonal inverse Hf5Cu3Sn-type structure (Pearson symbol hP18, space group P6(3)/mcm, a = 9.7139(11)-9.5438(16) angstrom, c = 6.4883(7)-6.4089(angstrom) A for RE = La-Nd), containing chains of face-sharing Mn-centered octahedra. Sm2Mn3Bi6 adopts a new monoclinic structure type (Pearson symbol mP22, space group P2(1)/m, a = 10.3917(8) angstrom, b = 4.4557(3) angstrom, c = 13.2793(10) angstrom, beta = 108.0100(10)degrees) in which the Mn centers are coordinated by Bi atoms in diverse geometries (distorted octahedral, trigonal bipyramidal, and distorted tetrahedral (seesaw)) and participate in extensive metal-metal bonding in the form of chains of Mn-3 clusters. Homoatomic bonding interactions involving nominally anionic Bi atoms are manifested as one-dimensional Bi chains in RE3MnBi5 and as four-atom-wide Bi ribbons in Sm2Mn3Bi6. Electrical resistivity measurements on single crystals revealed metallic behavior with prominent transitions near 40 K for RE3MnBi5 and 50 K for Sm2Mn3Bi6. Magnetic susceptibility measurements showed that Pr3MnBi5 undergoes magnetic ordering near 25 K.