To show that the transform
x → x = (2x₁ - x₂ - x₃ , x₁ - x₂ , x₂ - 2x₃), x = (x₁ , x₂ , x₃)³
x → x = (2x₁ - x₂ - x₃ , x₁ - x₂ , x₂ - 2x₃), x = (x₁ , x₂ , x₃)³