The isostructural title compounds are synthesized from dendritic Y or Er (R), sublimed RBr3, and Os in welded Nb containers at 850-1020-degrees-C. The crystal structure of Y4Br4Os has been established by single-crystal X-ray means (C2/c, Z = 8; a = 12.514 (5) angstrom, b = 12.381 (4) angstrom, c = 6.567 (2) angstrom, beta = 90.96 (3)-degrees; R, R(W)(F) = 3.5, 3.9%). The structure consists of osmium-centered antiprisms that share opposed square faces to generate quasi-infinite chains, viz., Y8/2(Os)Br4. Successive shared faces are tilted in opposite directions by approximately +/- 4-degrees, and the bromine atoms are displaced from coplanar positions in the direction of the tilt so as to cap four adjoining metal triangles on the shorter side of each antiprismatic unit. A fourth, comparable interchain Y-Br(a-i) bond is also formed by every Y and Br atom. The face-sharing square antiprismatic building blocks, the face capping of triangular cluster faces by halogen, and the intimate interchain bridging are all new for centered cluster halides. The need for distortion to gain the interchain bonding, the advantages of face capping of centered antiprismatic polyhedra, and the different behavior of the isoelectronic Ta4Te4Si are considered. Y4Br4Os exhibits a small Pauli-like paramagnetism.