Combinatorial equivalence of real moduli spaces
  A well-known construction of associahedra comes from truncations of simplices. Motivated by compactifications of point configurations, we show associahedra as truncations of certain products of simplices. This is then used to provide a combinatorial construction of the real moduli space of spheres relating it to blow-ups of the braid hyperplane arrangement. 
Satyan L. Devadoss