Suppose we have an $n$-dimensional convex polytope $\mathbf{P}$ represented by an intersection of half-spaces as the following:
\begin{equation} \mathbf{P} = \{ x \in \mathbb{R}^n \mid x \in \bigcap_{i=1}^K H_i \} \end{equation}
Then let's say that the set of all vertices of $\mathbf{P}$ is given by $V=(v_1,v_2,\ldots,v_N)$.
How we can find the relation between the number of halfspaces (i.e. $K$) and the number of vertices ($N$) of $\mathbf{P}$ ?
Thank you!