The re-examination of the crystal structure of α-hexagonal BaAl₂Si₂O₈ has revealed that the true symmetry of the crystal is lower than hexagonal-possibly, orthorhombic with a body centered lattice of dimensions: a=5.293, b=9.168 and c=7.79×2Å, and the crystals invariably occur in a trilling form made up by three orthorhombic individuals, simulating a hexagonal symmetry. Since it was not possible to distinguish the reflexions of each individual crystal from those of the others, the avarage structure with the hexagonal lattice, a=5.293, c=7.790Å, was investigated by the use of three-dimensional Fourier methods. The structure thus determined shows that the hexagonal (Al₂Si₂)O₈ sheets, which were reported in the previous work, are not exactly as such but trigonal owing to a slight deformation. In the structure, the barium atoms are coordinated by six oxygen atoms with the distance of 2.89Å, and the Si1/2Al1/2-O distances vary from 1.65 Å to 1.67 Å, giving the mean value of 1.66₅ Å.
A closer examination of the structure of the β-form on the basis of X-ray powder diffraction patterns and oscillation photographs taken at temperatures above 300°C. appears to disclose that the structure of the form is exactly hexagonal with a=5.313Å, c=7.805 Å (at about 450°C.). The space group is D¹_6h and there is one formula unit per cell. Thus the (Al₂Si₂)O₈ sheets in this form display a regular hexagonal symmetry, and the α-β inversion would be adequately explained as due to the change in configurations of the (Al₂Si₂)O₈ sheets from hexagonal to trigonal and vice versa.