  We study the generation number of massless fermions in compactifications
recently found in heterotic supergravity. The internal spaces are products of
two-dimensional spaces of constant curvature, and the standard embedding is not
assumed. The generation number is constrained by the equations of motion and
the Bianchi identity. In the case that the Euler characteristics of the three
internal submanifolds are $(2,-2,-2)$, the generation number is three or less.
We also show that three-generation solutions exist for arbitrary Euler
characteristics of the negatively curved 2-manifolds, and we present some
explicit solutions.
