Face of a polyhedral cone

A face of a polyhedral cone $C$ is $C\cap \ker \ell$ for a linear functional nonnegative on $C$. Every convex face of a polyhedral cone is exposed in this way. Faces include the whole cone and its lineality space, and are closed under intersection.

// Target: geometry-and-topology.bigb

A ray of a fan is a one-dimensional cone in a fan in toric geometry. It has the form ${\mathbb{R}}_{\ge 0}v$, where $v$ is a primitive lattice vector, and occurs as a face of a polyhedral cone.

A ray of a fan is a one-dimensional cone. It has a unique primitive lattice generator $v_{\rho }$ pointing along it.