Robert Dawson - What shape is a loaded die?

In this talk, I will describe work done by Wendy Finbow and myself on the geometry of regular polytopes. We call a polytope loadable if it contains a point P that is above only one facet F; if such a polytope is constructed with nonuniform density so that its center of gravity is at P, and is stood on a horizontal hyperplane, it will topple from any other facet onto F. We classify the loadable regular polytopes, and illustrate, as far as possible, where the center of gravity must go to accomplish the loading.