<p>Highly porous piezoelectric metamaterials, which have recently become possible to create using additive technologies, can demonstrate unique characteristics, since they consist of blocks located in various spatial directions and can have different polarization. Here, we investigate the effective properties of the best-known foam cell in the form of asymmetric Gibson–Ashby cell and regular lattice composed of such cells. Variants of piezoceramic cells and lattices with uniform polarization and with three models of inhomogeneous polarization, as well as cases of cells and lattices with canonical, with minimum and with maximum frame sizes are considered. A detailed analysis of their effective stiffness moduli, permittivities and piezomoduli is given. Among the most interesting results, it can be noted that the moduli associated with two directions perpendicular to the polarization axis can differ significantly, and the effective piezomoduli of stress, charge and voltage can change signs.</p>