The goal of the talk is to show you a beautiful matrix and then to explain its geometric significance. This will enable me to explain why two rival geometric interpretations of `Reid's recipe' are equivalent. To begin, I'll set the scene by discussing the classical McKay correspondence in dimension two and I'll go on to discuss how this extends naturally to dimension three. I'll introduce Reid's recipe by studying a resolution of C^3 by an action of the cyclic group of order
19 that gives rise to the beautiful matrix. I'll reveal the geometry that this matrix encodes, and as a result, we'll see that two conjectures for certain toric algebras arising in strong theory are equivalent.