  We continue the classification of the fermionic Z2XZ2 heterotic string vacua
with symmetric internal shifts. The space of models is spanned by working with
a fixed set of boundary condition basis vectors and by varying the sets of
independent Generalized GSO (GGSO) projection coefficients (discrete torsion).
This includes the Calabi-Yau like compactifications with (2,2) world-sheet
superconformal symmetry, as well as more general vacua with only (2,0)
superconformal symmetry. In contrast to our earlier classification that
utilized a montecarlo technique to generate random sets of GGSO phases, in this
paper we present the results of a complete classification of the subclass of
the models in which the four dimensional gauge group arises solely from the
null sector. In line with the results of the statistical classification we find
a bell shaped distribution that peaks at vanishing net number of generations
and with ~15% of the models having three net chiral families. The complete
classification reveals a novel spinor-vector duality symmetry over the entire
space of vacua. The S <-> V duality interchanges the spinor plus anti-spinor
representations with vector representations. We present the data that
demonstrates the spinor-vector duality. We illustrate the existence of a
duality map in a concrete example. We provide a general algebraic proof for the
existence of the S <-> V duality map. We discuss the case of self-dual
solutions with an equal number of vectors and spinors, in the presence and
absence of E6 gauge symmetry, and present a couple of concrete examples of
self-dual models without E6 symmetry.
