  New results are presented for the degeneracy condition of elastic waves in
anisotropic materials. The existence of acoustic axes involves a traceless
symmetric third order tensor that must vanish identically. It is shown that all
previous representations of the degeneracy condition follow from this acoustic
axis tensor. The conditions for existence of acoustic axes in elastic crystals
of orthorhombic, tetragonal, hexagonal and cubic (RTHC) symmetry are
reinterpreted using the geometrical methods developed here. Application to
weakly anisotropic solids is discussed, and it is shown that the satisfaction
of the acoustic axes conditions to first order in anisotropy does not in
general coincide with true acoustic axes.
