  The number of rational points in toric data are given for two-parameter
Calabi-Yau $n$-folds as toric hypersurfaces over finite fields $\mathbb F_p$ .
We find that the fundamental period is equal to the number of rational points
of the Calabi-Yau $n$-folds in zeroth order $p$-adic expansion. By analyzing
the solution set of the GKZ-system given by the enhanced polyhedron, we deduce
that under type II/F-theory duality the 3D and 4D Calabi-Yau manifolds have the
same number of rational points in zeroth order. Taking the quintic and its
duality as an example, the number of rational points in some specific complex
moduli are given by numerical calculation to support our results.
