  Reflexive polytopes have been studied from viewpoints of combinatorics,
commutative algebra and algebraic geometry. A nef-partition of a reflexive
polytope $\mathcal{P}$ is a decomposition
$\mathcal{P}=\mathcal{P}_1+\cdots+\mathcal{P}_r$ such that each $\mathcal{P}_i$
is a lattice polytope containing the origin. Batyrev and van Straten gave a
combinatorial method for explicit constructions of mirror pairs of Calabi-Yau
complete intersections obtained from nef-partitions. In the present paper, by
means of Gr\"{o}bner basis techniques, we give a large family of nef-partitions
arising from unimodular configurations.
