Triclinic elastic anisotropy contains at most 16 isolated singularities. The singularities can be in real or complex directions. If we count both real and complex singularities and their multiplicities, the total number of singularities is always 16 regardless of symmetry or strength of anisotropy. The real singularities describe the propagation of homogeneous plane waves, the complex singularities describe the propagation of inhomogeneous plane waves. The real singularities generate a linear polarization of waves in their vicinity. The complex singularities generate an elliptical polarization. The triclinic anisotropy with 6-10 real acoustic axes is most common. Examples of media with no or 16 real singularities are presented.
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