  We provide a new tool to interpret the large scale structure of the Universe.
As suggested in Paper II, energy density filaments could have been produced by
subjacent magnetic flux tubes when the Universe was dominated by radiation. In
more recent time epochs, small scale filaments have evolved in a complicated
way, but large scale filaments have probably survived and should be identified
with present observed matter filaments of clusters. A primordial magnetic field
lattice made up of magnetic flux tubes would then have originated a matter
lattice made up of cluster filaments. Taking into account some restrictions in
the magnetic field configuration we speculate what type of matter network this
would have generated. The simplest lattice is made up of octohedra connected at
their vertexes, reminding us of a structure of superimposed egg cartons. The
vertexes would correspond to large superclusters, which would therefore have
eight filaments emerging from them. Some observational evidence is found in the
Local Supercluster, which is spider-like, with eight legs.
