  The piezoelectricity law is a constitutive model that describes how
mechanical andelectric fields are coupled within a material. In its linear
formulation this law comprises threeconstitutive tensors of increasing order:
the second order permittivity tensor S, the third orderpiezoelectricity tensor
P and the fourth-order elasticity tensor C. In a first part of the paper,the
symmetry classes of the piezoelectricity tensor alone are investigated. Using a
new approachbased on the use of the so-called clips operations, we establish
the 16 symmetry classes of thistensor and provide their associated normal
forms. Second order orthogonal transformations(plane symmetries and $\pi$-angle
rotations) are then used to characterize and classify directly 11out of the 16
symmetry classes of the piezoelectricity tensor. An additional step to
distinguishthe remaining classes is proposed
