The associahedron is a polytope whose graph is the graph of flips on triangulations of a convex polygon. Pseudotriangulations and multitriangulations, which generalize triangulations in two different ways, can both be interpreted via duality as pseudoline arrangements with contacts supported by a given network. In this talk, I will present the construction of the "brick polytope" of a sorting network. The graph of this polytope realizes a subgraph of the flip graph on pseudoline arrangements supported by the network. In particular, for certain well-chosen networks, our brick polytopes coincide with Hohlweg & Lange's associahedra. Joint work with Francisco Santos (Universidad de Cantabria).