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This book deals with necessary and sufficient conditions for the existence of axes and planes of symmetry. We discuss matrix representation of an elasticity tensor belonging to a trigonal, a tetragonal or a hexagonal material. The planes of symmetry of an anisotropic elastic material (if they exist) can be found by the CowinMehrabadi theorem (1987) and the modified CowinMehrabadi theorem proved by Ting (1996). Using the CowinMehrabadi formalism Ahmad (2010) proved the result that an anisotropic material possesses a plane of symmetry if and only if the matrix associated with the material commutes with the matrix representing the elasticity tensor. A necessary and sufficient condition to determine an axis of symmetry of an anisotropic elastic material is given by Ahmad (2010). We review the CowinMehrabadi theorem for an axis of symmetry and develop a straightforward way to find the matrix representation for a trigonal, a tetragonal or a hexagonal material.
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