Hybrid CPbX₃ (C=Cs, CH₃NH₃; X=Br, I) perovskites are blessed with both excellent photovoltaic properties and high toxicity that hinders their practical application. Unfortunately, all Pb-free alternatives based on Sn and Ge are extremely unstable. Although stable and non-toxic C₂ABX₆ double-perovskites based on alternating corner-shared AX₆ and BX₆ octahedra (where A=Ag, Cu; B=Bi, Sb) are possible, they have indirect and wide bandgaps of over 2 eV. However, is it necessary to keep the corner-shared perovskite structure to retain good photovoltaic properties? Here, we demonstrate another family of photovoltaic halides based on edge shared AX₆ and BX₆ octahedra with the general formula AaBbXx (x=a+3b) such as Ag₃BiI₆, Ag₂BiI₅, AgBiI₄, AgBi₂I₇. As perovskites were named after their prototype oxide CaTiO₃ discovered by Lev Perovski, we propose to name these new ABX halides as rudorffites after Walter von Rudorff who discovered their prototype oxide NaVO₂. We studied structural and optoelectronic properties of several highly stable and promising Ag-Bi-I photovoltaic rudorffites that feature direct bandgaps in the range of 1.79-1.83 eV and demonstrated a proof-of-concept FTO/c-m-TiO₂/Ag₃BiI₆/PTAA/Au solar cell with photo-conversion efficiency of 4.3%.