Bott-Samelson varieties are twisted products of $\mathbb{CP}^1$'s with a map into $G/B$. This talk will be about brick varieties which are the general fibers of Bott-Samelson maps. I will describe the moment polytopes of the brick varieties and describe some instances in which these varieties are toric. In particular, I will give a description of the toric variety of the associahedron.