We have learned that a polyhedron is the sum of a polytope and a polyhedral cone, but how do you know this graphically?
For example if you're a given polyhedron on paper and you have to determine which part is the polytope and which part is the cone, how do you do that?
I have looked in my notes and can't find anything on this.
Do you know any graphical examples?
A polyhedron can either be bounded, and in this case it is called a polytope, or it can be unbounded, and it is then a polyhedral cone.
Saying that a polyhedron is the sum of a polytope and a polyhedral cone is just another way of saying this.
Graphically, if the polyhedron is "opened" it is a polyhedral cone, and if it is closed, it is a polytope.