The title single-crystal (icosamagnesium dodecaaluminium icosazinc), was obtained during the synthesis of an Mg–Al–Zn alloy at high pressure and temperature. It crystallizes in space group Im3 (No. 204) with seven distinct metal-atom sites: three are occupied by aluminium and zinc, one by zinc and magnesium and three by magnesium (two partially occupied). One of the Al/Zn sites has icosahedral coordination. There are significant difference between the current model and that of previous studies [Montagné & Tillard (2016). J. Alloys Compd. 656, 159–165].