We propose a general and complete classification of all possible new and old kinds of surface plasmon waves that can propagate at boundaries of arbitrary linear, local bi-anisotropic media, including the quartic metamaterials. For arbitrary frequency, wavelength, propagation direction, penetration depths and fields of the proposed surface plasmon waves we found the dispersion condition and determined the 72-parametric class of media that support a particular surface plasmon. A member of each class is a pair of anisotropic materials without magnetoelectric couplings.
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