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We describe novel topological phases of iso-frequency k-space surfaces inbi-anisotropic optical materials - tri- and tetra-hyperbolic materials, whichare induced by introduction of chirality. This completes the classification ofiso-frequency topologies for bi-anisotropic materials, since as we show alloptical materials belong to one of the following topological classes: tetra-,tri-, bi-, mono- or non-hyperbolic. We show that phase transitions betweenthese classes occur in the k-space directions with zero group velocity at highk-vectors. This classification is based on the sets of high-k polaritons(HKPs), supported by materials. We obtain the equation describing these setsand characterize the longitudinal polarization impedance of HKPs.

Tri- & Tetra-Hyperbolic Iso-frequncy Topologies Complete Classification of Bi-Anisotropic Materials