In the current paper isofrequency surface of a hypercrystal made from semiconductor and ferrite based metamaterials is studied numerically and theoretically. The particular attention is devoted to studying the ranges when singularity points on the isofrequency surface occur. Such conditions take place when isofrequency surfaces for TE-polarized and TM-polarized waves intersect. Depending on type of intersecting wave surfaces (open hyperbolic or closed ellipsoid), the resulting topological singularities may lead to the specific surface states existence or conical refraction phenomenon. The physical properties of the considered phenomena are mainly determined by the electrodynamical properties of the hypercrystal under study and, thus, can be effectively tuned by means of external magnetic field value, frequency and semiconductor and/or ferrite filling factor. It has been shown, that due to the peculiarities of the considered system, unique isofrequency topologies, like bi-hyperbolic surfaces, may arise.