I'll describe a combinatorial/geometric construction which I call the plaid model, on account of its resemblance to the weave in a plaid shirt. For each rational number the model produces a union of embedded polygonal surfaces in a cube. I will explain how you recover the dynamics of outer billiards on kites when you slice the model in one direction and how you recover some of Pat Hooper's Truchet tiling system when you slice the model 2 other directions. The model is a kind of marriage of these two seemingly unrelated dynamical systems, and has a rich structure in its own right. I'll show off the main results with plenty of color computer demos. Speaker(s): Rich Schwartz (Brown University)