My Optimization book defines a polyhedron as an intersection of finitely many half-spaces, and a polytope $P$ is defined as a bounded polyhedron. The book then goes on to talk about the edges and the non-degenerate vertices, but it does not define these terms (altough it does define a vertex as a point of $P$ which is not the convex combination of any two points in $P$). Could you please enlighten me to the definition of these two terms?
My Idea:
In $\mathbb{R}^2$, an edge of the polytope is a one of the actual hyperplanes defining the polytope. In $\mathbb{R}^3$, an edge of the polytope is the intersection of any two of the hyperplanes defining the polytope. My idea is that in $\mathbb{R}^n$, an edge of the polytope is the intersection of any $n-1$ hyperplanes defining the polytope.
As far as degenrate vertex, I really don't know. Based on the context, I think the following is an example of a degenerate vertex: consider a polytope in $\mathbb{R}^2$ which is just a line segment. Then its endpoints are degenerate vertices.