We report the temperature T dependence of the proton Zeeman relaxation rate R in solid t-butylbenzene at 8-50, 22.5 and 53.0MHz. The relaxation is caused by the modulation of the spin-spin dipole-dipole interactions by the reorienting t-butyl groups and their constituent methyl groups. It is shown that even if the phenyl group reorients, it makes a very small contribution to the observed relaxation rate. The observed R versus T is very complicated and this is unusual for such simple solids as t-butylbenzene. The data are fitted with several models for the dynamical properties of the t-butyl group and its constituent methyl groups, each assuming a particular symmetry imposed by the crystal structure.