Definition
- A \(\mathcal V\)-polytope is the convex hull of a finite set of points \(P\subset \mathbb R^d\).
- A \(\mathcal H\)-polyhedron is the intersection of finitely many affine half-spaces in \(\mathbb R^d\)
- An \(\mathcal H\)-polytope is a bounded \(\mathcal H\)-polyhedron
- A polytope is a set of points \(P\subset \mathbb R^d\) which can be presented either as a \(\mathcal V\)-polytope or a \(\mathcal H\)-polytope.
- Polytopes are necessarily compact, polyhedra are not.