Abstract: Given a reduced crystallographic root system with a fixed simple system, it is associated to a Weyl group $W$ and a polytope $P$ which is the convex hull of the $W$-orbit of a dominant weight. $P$ and $P/W$ are polytopes, associated with complex toric varieties $X_P$ and $X_{P/W}$ respectively. We will see a homotopy equivalence between $X_P/W$ and $X_{P/W}$, and contractibility of the real real points $X_{P}^{\mathbb{R}}/W$ for small ranks.