An interval representation is a set of intervals on the real line, ordered by x<y if the interval x lies entirely to the left of the interval y. An interval order is a partially ordered set which is isomorphic to some interval representation. There are a number of ways to generalize the class of interval orders to larger classes of ordered sets. The method of generalization I will be talking about is a continuation of work done by Stephen Ryan, and motivated by a paper by Habib, Kelly, and Mhring. I replace the intervals with n-dimensional polytopes indexed by certain parameters. In this way I define a large number of classes of ordered sets. I have asked which of these classes is contained in another of these classes, and I have many answers and many unanswered questions.