Abstract The crystal structure of the hexagonal Zn 3MgY phase has been determined by single-crystal X-ray diffraction. The structural model, refined to a final R value of 0.047, has the composition Zn 60.68Mg 18.28Y 21.04, a=9.082(2) Å and c=9.415(5) Å and the space group P6 3/ mmc. Among the 36 atomic sites 28 (or 77.8%) are icosahedrally coordinated (heavily distorted by the large Y atoms) and occupied by Zn and Mg (not all) atoms. As the interatomic distance between the centers of a pair of icosahedra increases from 2.6 to 3.1 Å, 4.7 to 4.8 Å, to 6.4 Å, their connection changes from interpenetration, face-sharing, to vertex-sharing. The structure of Zn 3MgY is characterized by a layer structure consisting of FP( FP)’ layers stacked along the c axis, where F and P denote flat and puckered layers, respectively, and ( FP)’ is related to FP by a 6 3 screw. The Zn3 icosahedra, in the PFP’ layer block, are fused into pairs in the 〈1 0 0〉 directions. On the other hand the Zn1, Zn2, and Mg/Zn icosahedra form vertex-sharing, face-sharing, or interpenetrated chains in the [0 0 1] direction.