<p>The results of studies of NMR and spin relaxation in solids are systematized and discussed under the conditions when three or more nuclei of single species are simultaneously involved in the elementary event of their dipole interactions but not two nuclei as is ordinarily the case. Such interactions are clearly manifested in the magically oriented singly, doubly, and triply rotating frames (RFs). A number of effects in RFs NMR and spin relaxation are described which are explicitly specified by the many-spin homo-nuclear dipolar interactions. The studies were carried out by the method of direct recording of NMR in the strong effective magnetic field in the single magic-angle RF at comparatively low-resonance frequency. A modification of the standard coherent pulsed NMR spectrometer is described, which makes it capable to carry out similar measurements at the high frequency in a large polarizing magnetic field. In contrast to the low-frequency direct method, the measurements by the modified high-frequency one are carried out point-by-point by multiple repetitions of the experiment, much as the spin–lattice relaxation time is measured in the single-resonant RF in the standard continuous spin-locking experiments.</p>