  We classify the subgroups of the automorphism group of the product of 4
projective lines admitting an invariant anticanonical smooth divisor on which
the action is free. As a first application, we describe new examples of
Calabi-Yau 3-folds with small Hodge numbers. In particular, the Picard number
is 1 and the number of moduli is 5. Furthermore, the fundamental group is
non-trivial. We also construct a new family of minimal surfaces of general type
with geometric genus zero, K^2=3 and fundamental group of order 16. We show
that this family dominates an irreducible component of dimension 4 of the
moduli space of the surfaces of general type.
