We report measurements of the de magnetization, the low-held ac magnetic susceptibility, and the electrical resistivity of large (up to 0.5 cm(3)) single-grain samples of icosahedral R-Mg-Zn (R = Y, Tb, Dy, Ho, and Er). The dc magnetization and ac magnetic susceptibility data both indicate that icosahedral Tb-Mg-Zn and Dy-Mg-Zn undergo a transition to a spin-glass state at T-f = 5.8 and 3.6 K, respectively, while low-temperature ac susceptibility measurements show that T-f = 1.95 and 1.3 K for Ho-Mg-Zn and Er-Mg-Zn, respectively. For the series of solid solutions (Y1-xTbx)-Mg-Zn, the freezing temperature T-f varies approximately as x(2/3). The (Y1-xGdx)-Mg-Zn solid solutions have lower T-f values than (Y1-xTbx)-Mg-Zn for the same magnetic rare-earth concentrations (x), indicating that local moment anisotropy caused by crystalline electric-field effects plays a significant role in increasing T-f. On the other hand, angular-dependent studies show that the de magnetization for T > T-f is isotropic within the experimental uncertainty. The electrical resistivity rho(T) of the single-grain samples is only weakly temperature dependent, with a small, negative d rho/dT. Absolute values of the resistivity fall in the range between 150 and 200 mu Omega cm, which is distinctly lower than the values previously reported for other thermodynamically stable icosahedral quasicrystals. [S0163-1829(99)05801-4].