The authors review the basic theory governing the existence of exceptional bulk waves which propagate in an infinite anisotropic elastic medium while leaving a family of parallel planes traction-free. A solution scheme proposed by Al’shits and Lothe is implemented numerically and solution lines of exceptional waves for tetragonal tellurium dioxide are computed as an example. It is found that tellurium dioxide possesses nine acoustic axes, five great circles on the unit sphere as solution lines of transverse exceptional waves, and a number of closed curves as solution lines of non-transverse exceptional waves.

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