A convex body $V$ consisting of half-lines issuing from one point — the apex of the cone. The case when $V$ is identical with the entire space is excluded from this definition. The concept of a convex cone includes that of a dihedral angle and a half-space as special cases. A convex cone is sometimes meant to be the surface of a convex cone.
Convex cone. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Convex_cone&oldid=38947