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