• ## $$d$$ hyperplanes intersection bounds

We bound the position of the $$0$$-cells of an arrangement of hyperplanes in $$\mathbb{R}^d$$. This allows, for example, to build an hypercube that intersects all cells of the arrangement. Such an hypercube must contain at least one point of each cell of the arrangement. When $$q > 0$$, in order...

• ## Polyhedral sets

A polyhedral set set in $$\mathbb{R}^d$$ is the intersection of a finite number of closed halfspaces, and a (convex) polytope is a bounded polyhedral set. This definition of a polytope is called a halfspace representation (H-representation or H-description). A defining halfspace of a polyhedral set $$P$$ is a facet-defining halfspace...