Integral affine structures on spheres and torus fibrations of Calabi-Yau toric hypersurfaces II

This paper is a continuation of our paper math.AG/0205321 where we have built a combinatorial model for the torus fibrations of Calabi-Yau toric hypersurfaces. This part addresses the connection between the model torus fibration and the complex and K"ahler geometry of the hypersurfaces.