By Richard LeComte
Benjamin Braun, associate professor of mathematics in the University of Kentucky’s College of Arts & Sciences, received a $150,000 grant from the National Science Foundation to research geometric objects called polytopes.
Examples of polytopes are two-dimensional polygons; three-dimensional cubes, pyramids and prisms; and higher-dimensional extensions of these objects. Polytopes are used to find solutions for transportation problems, model possible outcomes of elections and investigate biological phenomena. Geometric properties of polytopes help planners model problems using computers and thus solve complicated problems. For example, volumes of polytopes can be used to compute the chance that a voting paradox will happen for a voting system.
“Polytopes have been