This talk will give a geometric interpretation for the embedding of the Kreweras lattice of non-crossing partitions into the Cayley graph of the symmetric group. Toric geometry gives a presentation of the equivariant cohomology ring of the flag variety GL/B as polynomial-valued functions on the symmetric group, subject to certain “edge conditions” from the Cayley graph. With Nantel Bergeron, Philippe Nadeau, Hunter Spink, and Vasu Tewari, I have found a sub variety of GL/B with an analogous description in terms of the Kreweras lattice. We develop the non-crossing combinatorics of this space and show that its cohomology ring has natural connections to other areas of algebraic combinatorics including the ring of quasisymmetric polynomials, Schubert calculus, and the forest polynomials recently introduced by Tewari and Nadeau.