Isothermal ageing of plastically deformed Mg-Zn-Y alloys resulted in precipitation along twin boundaries. The bulky precipitates so formed had structures similar to those recently reported for the rod-like precipitates, but afforded a more detailed study by high-resolution TEM due to their larger size. The core of the precipitates often had the structure of the monoclinic Mg₄Zn₇ phase, and had the orientation ; with either the matrix or the twin. On this Mg₄Zn₇ phase, the hexagonal MgZn₂ phase grew in two orientations, both with . One of these orientations formed a known orientation relationship ; with the matrix. The part of the precipitate with the MgZn₂ structure was usually in direct contact with the twin boundary. Both the Mg₄Zn₇ and MgZn₂ phases have layered structures that can be described with similar building blocks of icosahedrally coordinated atoms. The atomic positions of zinc atoms comprise the vertices of these icosahedra and form ‘thick’ rhombic tiles. The orientations of these rhombuses remain unchanged across the interfaces between the two phases. Near the interface with MgZn₂, transition structures formed in the Mg₄Zn₇ phase, with the Zn:Mg atom ratio between those of the Mg₄Zn₇ and MgZn₂ phases. In these transition structures, the unit cell of the Mg₄Zn₇ phase is extended along [100] or [001] by half a unit cell length by continuation of the rhombic tiling. Structures of these extended unit cells are proposed.