  Torus-fibered Calabi-Yau threefolds Z, with base dP_9 and fundamental group
pi_1(Z)=Z_2 X Z_2, are reviewed. It is shown that Z=X/(Z_2 X Z_2), where X=B
X_{P_1} B' are elliptically fibered Calabi-Yau threefolds that admit a freely
acting Z_2 X Z_2 automorphism group. B and B' are rational elliptic surfaces,
each with a Z_2 X Z_2 group of automorphisms. It is shown that the Z_2 X Z_2
invariant classes of curves of each surface have four generators which produce,
via the fiber product, seven Z_2 X Z_2 invariant generators in H_4(X,Z). All
invariant homology classes are computed explicitly. These descend to produce a
rank seven homology group H_4(Z,Z) on Z. The existence of these homology
classes on Z is essential to the construction of anomaly free, three family
standard-like models with suppressed nucleon decay in both weakly and strongly
coupled heterotic superstring theory.
