We describe a family of genus one fibered Calabi-Yau threefolds with fundamental group Z/2. On each Calabi-Yau Z in the family we exhibit a positive dimensional family of Mumford stable bundles whose symmetry group is the Standard Model group 5C/(3) x SU(2) x U(l) and which have C3 = 6. We also show that for each bundle V in our family, C2(Z) -C2{V) is the class of an effective curve on Z. These conditions ensure that Z and V can be used for a phenomenologically relevant compactification of Heterotic M-theory.
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Donagi et al. (2001) studied this question.