  Clips is a binary operation between conjugacy classes of closed subgroups of
a compact group, which has been introduced to obtain the isotropy classes of a
direct sum of representations E1 $\oplus$ E2, if the isotropy classes are known
for each factor E1, E2. This allows, in particular, to compute the isotropy
classes of any reducible representation, once one knows the decomposition into
irreducible factors and the symmetry classes for the irreducible factors. In
the specific case of the three dimensional orthogonal group O(3), clips between
some types of subgroups of O(3) have already been calculated. However, until
now, clips between type II and type III subgroups were missing. Those are
encountered in 3D coupled constitutive laws. In this paper, we complete the
clips tables by computing the missing clips. As an application, we obtain 25
isotropy classes for the standard O(3) representation on the full 3D
Piezoelectric law, which involves the three Elasticity, Piezoelectricity and
Permittivity constitutive tensors.
