POLYTOPAL BALLS ARISING IN OPTIMIZATION

We study a family of polytopes and their duals, that appear in various optimization problems as the unit balls for certain norms. These two families interpolate between the hypercube, the unit ball for the ∞-norm, and its polar cross-polytope, the unit ball for the 1-norm. We study combinatorial and geometric properties of both families such as their f-vector, their volume, and the volume of their boundary.