Isotropic fourth-rank susceptibility (${\chi }_{ijkl}=a{\delta }_{ij}{\delta }_{kl}+b{\delta }_{ik}{\delta }_{jl}+c{\delta }_{il}{\delta }_{jk}$)

An isotropic fourth-rank polar tensor has the displayed form. If its three input slots are fully interchangeable at the same relevant frequency arguments, then $a=b=c$, giving ${\chi }_{xxxx}=3{\chi }_{xxyy}$. For mixed-sign or unequal frequencies, intrinsic permutation exchanges the arguments too; it need not make all coefficients at one fixed ordering equal.