  In this paper we construct a degeneration of Bott-Samelson-Demazure-Hansen
varieties to toric varieties in an algebraic family and study the geometry of
the resulting toric varieties. We give a natural set of torus invariant curves
that generate the Chow group of $1$-cycles of the limiting toric variety and
express the ample cone of this toric variety as a sub-cone of the ample cone of
the corresponding Bott-Samelson-Demazure-Hansen variety. We also give a
description of Extremal and Mori rays and determine when this toric variety is
Fano.
