Atomic structures of the precipitates in Al–Mg–Si alloys have important similarities. The trigonal precipitate U1-MgAl2Si2 has super-cells in both Al and diamond Si. U1 is related to the precipitates β′, U2, and B′ via silicon. The Si-content of the four precipitates can be described as triangular planes parallel to Al {1 0 0} or Al {3 1 0} planes. Large Si-particles frequently align two of their {1 1 1} planes in a similar way. In the Al–Mg–Si alloy system this correspondence explains most coherency relations between precipitates, and between precipitates and matrix. The connection with Si gives a unified view of the precipitate structures. A model is given for a reflection twin boundary in U1.