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 $t$.

Question. Can we exactly count the number of vertices in the polyhedron? If so, how to count it?

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 $r'$.

Question. Can we exactly count the number of vertices in the polyhedron? If so, how to count it?

Suppose $Ax\leq b$ is a polyhedron where number of rows in $A$ is $r$ and $x$ is in $\mathbb R^n$ and rank of $A$ is $t$ can we exactly count the number of vertices in the polyhedron? If so how to count?

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 $t$.

Question. Can we exactly count the number of vertices in the polyhedron? If so, how to count it?