  The heterotic string free fermionic formulation produced a large class of
three generation models, with an underlying SO(10) GUT symmetry which is broken
directly at the string level by Wilson lines. A common subset of boundary
condition basis vectors in these models is the NAHE set, which corresponds to
Z2 X Z2 orbifold of an SO(12) Narain lattice, with (h11,h21)=(27,3).
Alternatively, a manifold with the same data is obtained by starting with a Z2
X Z2 orbifold at a generic point on the lattice, with (h11,h21)=(51,3), and
adding a freely acting Z2 involution. The equivalence of the two constructions
is proven by examining the relevant partition functions. The explicit
realization of the shift that reproduces the compactification at the free
fermionic point is found. It is shown that other closely related shifts
reproduce the same massless spectrum, but different massive spectrum, thus
demonstrating the utility of extracting information from the full partition
function. A freely acting involution of the type discussed here, enables the
use of Wilson lines to break the GUT symmetry and can be utilized in
non-perturbative studies of the free fermionic models.
