We presented proofs that show that there are only eight symmetry classes of a Hookean solid, and that their hierarchy is only partially ordered.

Our proofs are based on group theory.

Without this work, many seismologists implicitly assumed that there would be a possibility of extending the number of symmetry classes as could be necessary to accommodate modelling needs.

Also, many seismologists assumed a sequential hierarchy proceeding from the general anisotropy to isotropy.

The recognition of these intrinsic properties of a Hookean solid allows for a reliable interpretation of seismic models, which — for the most part — are based on such a solid.

Bóna, A., Diner, Ç., Kochetov, M., Slawinski, M.A. (2010) On symmetries of elasticity tensors and Christoffel matrices . arXiv:1011.4975

Bóna, A., Bucataru, I., Slawinski, M.A. (2008) Space of SO(3)-orbits of elasticity tensors . Archives of Mechanics 60(2), 121–136

Bóna, A., Bucataru, I., Slawinski, M.A. (2004) Characterization of elasticity-tensor symmetries using SU(2). Journal of Elasticity 75(3), 267–289

Bóna, A., Bucataru, I., Slawinski, M.A. (2004) Material symmetries of elasticity tensors . The Quarterly Journal of Mechanics and Applied Mathematics 57(4), 583–598

Bos, L.P., Gibson, P.C., Kochetov, M., Slawinski, M.A. (2004) Classes of anisotropic media: A tutorial. Studia Geophysica and Geodætica 48, 265–287