  A stacking operation adds a $d$-simplex on top of a facet of a simplicial
$d$-polytope while maintaining the convexity of the polytope. A stacked
$d$-polytope is a polytope that is obtained from a $d$-simplex and a series of
stacking operations. We show that for a fixed $d$ every stacked $d$-polytope
with $n$ vertices can be realized with nonnegative integer coordinates. The
coordinates are bounded by $O(n^{2\log(2d)})$, except for one axis, where the
coordinates are bounded by $O(n^{3\log(2d)})$. The described realization can be
computed with an easy algorithm.
  The realization of the polytopes is obtained with a lifting technique which
produces an embedding on a large grid. We establish a rounding scheme that
places the vertices on a sparser grid, while maintaining the convexity of the
embedding.
