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The topology of isofrequency surfaces of a magneticsemiconductor superlattice influenced by an external static magnetic field is studied. In particular, in the given structure, topology transitions from standard closed forms of spheres and ellipsoids to open ones of Type I and Type II hyperboloids as well as bi-hyperboloids were revealed and analyzed. In the latter case, it is found out that a complex of an ellipsoid and bi-hyperboloid in isofrequency surfaces appears as a simultaneous effect of both the ratio between magnetic and semiconductor filling factors and magnetic field influence. It is proposed to consider the obtained bi-hyperbolic isofrequency surface as a new topology class of the wave dispersion.