A new series of isostructural ternary rare-earth zinc antimonides RE6Zn1+xSb14+y (RE = Pr, Sm, Gd-Ho) has been obtained by direct reaction of the elements at 1050-1100 degrees C. Single-crystal X-ray diffraction studies revealed that these compounds adopt an orthorhombic structure type (space group Immm, (no. 71), Z = 2, a = 4.28-4.11 angstrom, b = 15.15-14.73 angstrom, c = 19.13-18.56 angstrom in the progression from RE = Pr to Ho) that may be regarded as stuffed variants of a (U0.5Ho0.5)(3)Sb-7-type host structure. Columns of face-sharing RE6 trigonal prisms, centered by Sb atoms, occupy channels defined by an extensive polyanionic Sb network. This network is constructed from three-atom-wide and four-atom-wide Sb strips, the latter being linked together by single Sb atoms in RE6Zn1+xSb14 (RE = Sm, Gd-Ho; y = 0), but also by additional Sb-Sb pairs in a disordered fashion in Pr6Zn1+xSb14+y (y = similar to 0.6). Interstitial Zn atoms then partially fill tetrahedral sites (occupancy of 0.5-0.7) and, to a lesser extent, square pyramidal sites (occupancy of 0.04-0.12), accounting for the observed nonstoichiometry with variable x. Except for the Gd member, these compounds undergo antiferromagnetic ordering below T-N < 9 K, with the magnetic susceptibilities of the Tb, Dy, and Ho members following the Curie-Weiss law above T-N. For the Ho member, the thermal conductivities are low and the Seebeck coefficients are small and positive, implying p-type character consistent with the occurrence of partial Zn occupancies. At low temperatures (down to 5 K), electrical resistivity measurements for the Tb, Dy, and Ho members indicated metallic behavior, which persists at high temperatures (up to 560 K) for the Ho member. Band structure calculations on an idealized "Gd6Zn2Sb14" model revealed the existence of a pseudogap near the Fermi level.