  The first particle physics observable whose origin may be sought in string
theory is the triple replication of the matter generations. The class of Z2XZ2
orbifolds of six dimensional compactified tori, that have been most widely
studied in the free fermionic formulation, correlate the family triplication
with the existence of three twisted sectors in this class. In this work we seek
an improved understanding of the geometrical origin of the three generation
free fermionic models. Using fermionic and orbifold techniques we classify the
Z2XZ2 orbifold with symmetric shifts on six dimensional compactified internal
manifolds. We show that perturbative three generation models are not obtained
in the case of Z2XZ2 orbifolds with symmetric shifts on complex tori, and that
the perturbative three generation models in this class necessarily employ an
asymmetric shift. We present a class of three generation models in which the
SO(10) gauge symmetry cannot be broken perturbatively, while preserving the
Standard Model matter content. We discuss the potential implications of the
asymmetric shift for strong-weak coupling duality and moduli stabilization. We
show that the freedom in the modular invariant phases in the N=1 vacua that
control the chiral content, can be interpreted as vacuum expectation values of
background fields of the underlying N=4 theory, whose dynamical components are
projected out by the Z2-fermionic projections. In this class of vacua the
chiral content of the models is determined by the underlying N=4 mother theory.
