We introduce and produce experimentally optical beams exhibiting periodic skyrmionic polarization lattices at each transverse plane of propagation. These textures are meron lattices formed by tiles mapping hemispheres of the Poincaré sphere. All presented fields are combinations of a small number of plane waves. Firstly, we propose square lattices with a Skyrme density (the Jacobian of the mapping between the Poincaré sphere and physical space) that oscillates in sign but whose intensity distribution is constant. Secondly, we present triangular lattices preserving the Skyrme density's sign. Both lattices are invariant under propagation. Finally, we introduce a family of lattices with uniform Skyrme density sign, composed of square tiles that map to the same hemisphere of the Poincaré sphere. In these lattices, the polarization state undergoes a uniform local periodic rotation during propagation, thus preserving the texture's Skyrme density distribution.