The crystal structure of the solid electrolyte RbAg(4)I(5) has been determined from single-crystal x-ray diffraction counter data. There are four RbAg(4)I(5) in a cubic unit cell with a = 11.24 A. The structure refinement, by least squares, is based on space group P4(1)3 (O(7)). The arrangement of the iodide ions is similar to that of the manganese atoms in beta-manganese, and provides 56 iodide tetrahedra per unit cell, which share faces in such manner as to provide diffusion paths for the silver ions. The occurrence of the two low-temperature phases of RbAg(4)I(5) has been established by x-ray diffraction and optical examination.