Three-Loop Contribution to Hyperfine Splitting in Muonium: Polarization Corrections to Light by Light Scattering Blob

We calculate corrections of order ${\alpha }^3(Z\alpha )E_F$ to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with polarization insertions in the light by light scattering diagrams. This nonrecoil contribution turns out to be -2.63 Hz. The total contribution of all known corrections of order ${\alpha }^3(Z\alpha )E_F$ is equal to -4.28 Hz.