Anisotropic sublattices in cubic perovskite and their symmetry in multidimensional crystal space

Three tetragonal, partially occupied oxygen sublattices with a translational symmetry higher than the lattice translational symmetry can be introduced into the cubic perovskite structure. This higher symmetry is determined in the 9D space constructed on three orthogonal 3D subspaces corresponding to the sublattices. The generating matrices, metric tensors, and point symmetry matrices of this multidimensional space are determined. Irreducible stars of the representations of multidimensional space group are projected onto the irreducible stars of the space crystal group.