The compounds K3Bi3(PS4)(4) (I), K1.5Bi2.5(PS4)(3) (II), and KgBi(PS4)(4) (III) were synthesized, and their properties are described. Red needles of I crystallize in the tetragonal spacegroup P4/ncc with a = 21.0116(8) angstrom and c = 13.3454(10) angstrom and have a three-dimensional Bi/P/S framework structure with large channels occupied by K+ ions. Deep-red plates of 11 crystallize in the monoclinic super spacegroup P2/c(alpha(1/2 gamma))00 with a = 21.8034(12) angstrom, b = 8.8064(7) angstrom, c = 10.0333(6) angstrom, and beta = 90.004(5)degrees. This compound has an incommensurately modulated superstructure with the modulation vector q = 0.25a* + 0.5b* + 0.16c*. Bright-red irregularly shaped blocks of III crystallize in the orthorhombic space group P2(1)2(1)2 with a = 18.306(4) angstrom, b = 8.926(2) angstrom, and c = 9.710(2) angstrom and have a discrete molecular salt structure with mononuclear [Bi(PS4)(4)](9-) complexes. The structures reveal that as the relative amount of K3PS4 increases, there is a marked decrease in dimensionality of the framework. It was also possible to form a glass with the same stoichiometry as that of compound I. When annealed at 320 degrees C, the glass crystallized into compound II. The (31)p solid-state NMR spectra are reported, and they are consistent with the crystallographic results.