We derive a new upper bound on the diameter of a polyhedron , where . The bound is polynomial in and the largest absolute value of a sub-determinant of , denoted by . More precisely, we show that the diameter of is bounded by . If is bounded, then we show ...
The first example of a closed orientable hyperbolic 3-manifold was constructed by F. Lobell in 1931 from eight copies of the right-angled 14-hedron. We consider the family of hyperbolic polyhedra which generalize the Lambert cube and the Lobell polyhedron. ...
We investigate the diameter of a natural abstraction of the 1-skeleton of polyhedra. Although this abstraction is simpler than other abstractions that were previously studied in the literature, the best upper bounds on the diameter of polyhedra continue to ...
This thesis deals with the numerical modeling and simulation of granular media with large populations of non-spherical particles. Granular media are highly pervasive in nature and play an important role in technology. They are present in fields as diverse ...
Convex polyhedra are important objects in various areas of mathematics and other disciplines. A fundamental result, known as Minkowski-Weyl theorem, states that every polyhedron admits two types of representations, either as the solution set to a finite sy ...
