Injective Convex Polyhedra

Abstract

We characterize the convex polyhedra P in $${\mathbb {R}}^n$$Rn for which any family of n-dimensional axis-parallel hypercubes centered in P and intersected with P has the binary intersection property. The characterization is effective, concrete and convex geometric. As an application, we prove that the convex polyhedra determined by a finite linear system of inequalities with at most two variables per inequality are of this type. This provides in particular new examples of injective (or equivalently hyperconvex) metric spaces.