Projective cone

A projective cone (or just cone) in projective geometry is the union of all lines that intersect a projective subspace R (the apex of the cone) and an arbitrary subset A (the basis) of some other subspace S, disjoint from R.

In the special case that R is a single point, S is a plane, and A is a conic section on S, the projective cone is a conical surface; hence the name.