We present the theoretical principles of supercycled symmetry-based recoupling sequences in solid-state magic-angle-spinning NMR. We discuss the construction procedure of the SR26 pulse sequence, which is a particularly robust sequence for double-quantum homonuclear dipole-dipole recoupling. The supercycle removes destructive higher-order average Hamiltonian terms and renders the sequence robust over long time intervals. We demonstrate applications of the SR26 sequence to double-quantum spectroscopy, homonuclear spin counting, and determination of the relative orientations of chemical shift anisotropy tensors
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