Atoms in tetrahedral sites are shown in purple. Contrary to expectations based on ionic radius, in spinel the aluminum atoms are in octahedral sites and the magnesiums in the tetrahedral. Shown below is a polyhedral representation. Filled octahedra form criss-cross rows, with alternating layers of parallel rows offset as shown on the right side of the diagram. The square holes enclosed by the rows of octahedra are filled with tetrahedra.
Octahedral cations are in yellow and green, tetrahedral in purple.
Between oxygen layers we find hexagonal patterns of octahedral cations, and hexagonal patterns of tetrahedral cations with an octahedral cation at the center. A polyhedral view from the same direction is shown below. We can't reverse the roles of X and Y and fill all the sites. If we were to try, we could only fill half the octahedra with X, and the tetrahedra would only take up half the Y atoms. The remainder would fill the still-vacant octahedra.