Distances on Convex Bodies, Cones, and Simplicial Complexes

Abstract

A convex body in the n-dimensional Euclidean space \(\mathbb{E}^{n}\) is a compact convex subset of \(\mathbb{E}^{n}\). It is called solid (or proper) if it has nonempty interior. Let K denote the space of all convex bodies in \(\mathbb{E}^{n}\), and let K p be the subspace of all proper convex bodies.