M Theory Lesson 176

In Ben-Zvi's notes of recent work by Ben Webster et al (which he calls the cutting edge of mirror symmetry math) there is this diagram of a triangular arrangement of planes and its associated graph. The vertices represent the 7 regions of the Euclidean space and the edges an adjacency via an edge segment. Notice how this looks like a centered hexagon, or one side of a cube. This is a kind of Cayley graph. The permutations of four letters (which label the vertices of the permutohedron) also give a cubical Cayley graph. Koszul duality is about the correspondence between intersections of the planes and cones emanating from such points in the plane arrangement.