Suppose $Ax\leq b$ is a polyhedron, where the number of rows in $A$ is $r$, the vector $x$ lies in $\mathbb R^n$ and the rank of $A$ is $t$. Assume minimal number of hyperplane inequalities to define the polyhedron is $r'$.



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> **Question.** Can we exactly count the number of vertices in the polyhedron? If so, how to count it?
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Exactly counting number of vertices of a polyhedron
The answer varies according to the structure of the polytope. If you want the answer in particular cases, you can use vertex enumeration software, such as [lrs](http://cgm.cs.mcgill.ca/%7Eavis/C/lrs.html) .


