  We present simple mathematical solutions for optical fields that span all
nonparaxial polarization ellipses. These fields, given by a superposition of
five plane waves with non-coplanar polarizations, are experimentally
realizable. By slowly varying in time the relative amplitude between two groups
of plane waves, the resulting fields take the form of a periodic polarization
lattice, where all possible nonparaxial polarization ellipses are localized in
a 4D spatio-temporal cell. The field distributions in these cells can be
regarded as 4D skyrmionic textures.
