Recall (from a couple of years) that a "biroller" is the intersection of two perpendicular circular cylinders and takes an intriguing choatic path if rolled diagonally down a shallow, inclined (bathtub-like) trough. A "triroller" is the intersection of three perpendicular cylinders, with perhaps slightly less interesting rolling behavior. In either case, the roller can only change direction if it momentarily rests on the intersection of two ridges. Now consider the intersection of the four cones circumscribing a regular tetrahedron. (http://gosper.org/tetraroller1.gif, http://gosper.org/tetraroller2.gif). Instead of tipping on one of the triple points of ridges, it chooses left or right as it rolls up an initially nonexistent ridge. I'm not sure what would be the most entertaining surface, but these might make an even more hellish alternative to Gilbert & Sullivan's "elliptical billiard balls". The intersection ridges are in fact elliptical, and the projection along an altitude of the tetrahedron reveals quite probably a Reuleaux triangle (Wankel). The vector from the center to one of the triple points is exactly -3/5 times the vector to the opposite vertex. --rwg