  We construct one-parameter complex analytic families whose special fibers are
complete toric varieties. Under some assumptions, the general fibers of these
families also become toric varieties and we can explicitly describe the
corresponding fans from the data of the fans corresponding to the special
fibers. Using these families, we give a deformation family for a certain toric
weakened Fano 3-fold. Moreover, we get some examples of toric weakened Fano
4-folds.
