A parametrization is proposed for hexadecapole tensors, which observes symmetries coming from the O{sub h} group of transformations of the frame of reference defined through the quadrupole deformation and/or the rotation axes. A possible dependence of the hexadecapole deformation parameters on the quadrupole deformation is discussed. The inclusion of octupole deformation is considered. {copyright} {ital 1997} {ital The American Physical Society}