At high temperatures, BaTiO₃ has the cubic perovskite structure. On cooling, it undergoes a series of phase transitions in which the Ti atom moves away from the center of the TiO₆ octahedron, and there are changes in the space group and unit-cell parameters causing the ferroelectric behavior discussed in Chapter 8. Determine the number of twindomain variants (orientations) that could form in the first step when the cubic (a ≈ 4 Å, space group Pm₃m) structure undergoes a phase transition to a tetragonal structure with space group P4mm and cell parameters a = b ≈ c ≈ 4 Å, α = β = γ = 90°.