+ The dual of the cone of ``K`` at ``y`` is the dual face of the face
+ of ``K`` generated by ``y`` ([Tam]_ Corollary 3.2)::
+
+ sage: set_random_seed()
+ sage: K = random_cone(max_ambient_dim=8, max_rays=10)
+ sage: y = K.random_element()
+ sage: S = [y]
+ sage: phi_y = face_generated_by(K,S)
+ sage: points_cone_gens = list(K.rays()) + [-z for z in phi_y.rays()]
+ sage: points_cone = Cone(points_cone_gens, K.lattice())
+ sage: points_cone.dual().is_equivalent(dual_face(K, phi_y))
+ True
+
+ Since all faces of a polyhedral cone are exposed, the dual face of a
+ dual face should be the original face [HilgertHofmannLawson]_::
+
+ sage: set_random_seed()
+ sage: def check_prop(K,F):
+ ....: return dual_face(K.dual(), dual_face(K,F)).is_equivalent(F)
+ sage: K = random_cone(max_ambient_dim=8, max_rays=10)
+ sage: all(check_prop(K,F) for F in K.face_lattice())
+ True
+