We present 353 GHz full-sky maps of the polarization fraction p, angle ψ, and dispersion of angles S of Galactic dust thermal emission produced from the 2018 release of Planck data. We confirm that the mean and maximum of p decrease with increasing NH. The uncertainty on the maximum polarization fraction, pmax=22.0% at 80 arcmin resolution, is dominated by the uncertainty on the zero level in total intensity. The observed inverse behaviour between p and S is interpreted with models of the polarized sky that include effects from only the topology of the turbulent Galactic magnetic field. Thus, the statistical properties of p, ψ, and S mostly reflect the structure of the magnetic field. Nevertheless, we search for potential signatures of varying grain alignment and dust properties. First, we analyse the product map S×p, looking for residual trends. While p decreases by a factor of 3--4 between NH=1020 cm−2 and NH=2×1022 cm−2, S×p decreases by only about 25%, a systematic trend observed in both the diffuse ISM and molecular clouds. Second, we find no systematic trend of S×p with the dust temperature, even though in the diffuse ISM lines of sight with high p and low S tend to have colder dust. We also compare Planck data with starlight polarization in the visible at high latitudes. The agreement in polarization angles is remarkable. Two polarization emission-to-extinction ratios that characterize dust optical properties depend only weakly on NH and converge towards the values previously determined for translucent lines of sight. We determine an upper limit for the polarization fraction in extinction of 13%, compatible with the pmax observed in emission. These results provide strong constraints for models of Galactic dust in diffuse gas.
