Abstract: The present invention discovers the layup ofi. a multimaterial fully isotropic laminate that exhibits a concomitant stiffness isotropy in extension, shear, bending, and twisting; andii. a multimaterial quasi-homogeneous anisotropic laminate that has identical stiffness anisotropy in extension and bending as well as in shear and twisting.In addition, layups of the multimaterial fully isotropic laminate lead to a substantially new category of the single-material fully isotropic laminate.Although these laminate layups have distinctive applications as load-carrying structures, the approaches and models that generate these layups are closely related.