Polytopes Lectures on Polytopes Definitions (H-polytope, V-Polyhedron, V-Polytope, Cone, Conical Hull) Main Theorem (Minkowski–Weyl) Fourier-Motzkin Eliminiation (Theorem 1.2 Proof) (\(\mathcal{H}\)-polyhedron \( \iff \mathcal{V}\)-polyhedron) Farkas Lemma (I) Farkas Lemma (II) Faces of Polytopes Definitions