A polyhedral cone is the intersection of finitely many closed half-spaces whose bounding hyperplanes pass through the origin. Equivalently, it has the form
 |
where 
is a real matrix with 
columns and the inequality
is interpreted componentwise (Fukuda et al. 2007). It is a closed convex
cone.
For example, 
is a polyhedral cone, as is any subspace of 
. Thus a polyhedral cone may contain a whole line.
A cone is called rational when it admits such a description with a matrix
having rational entries.
