Quasicrystals form a class of materials presenting a long range order without translational symmetry. Understanding their local structure and dynamics is still challenging. Icosahedral Tsai-type quasicrystals were recently studied by coherent-incoherent neutron scattering1 and showed evidences for a dynamics of the central symmetry-breaking tetrahedron in the periodic approximant, and its phase transition was attributed to an ordering of the tetrahedra. These results open new questions about the coupling between the different shells of the rhombic triacontahedral units that are the building blocks of Tsai clusters in such approximant or quasicrystals. The potentialities of NMR in such samples, that combine metallic shifts and quadrupolar interactions, will be discussed from variable temperature 45Sc NMR experiments on the approximant, VOCS reconstruction of spectra, and 67Zn NMR results (observing such a nucleus is challenging due to a low gyromagnetic ratio and natural abundance (4.1%)), obtained at 18.8T (800MHz-TGIR Lille) and 300-600MHz in Rennes. 1.H. Euchner et al., J Phys: Condens. Matter 2012, 24, 415403