How many corners can a $n$-dimensinal convex polyhedron have at tops? Is it the same as the number of corners a $n$-dimensional simplex has?
EDIT: By polyhedron $P$, I mean, that for some matrix $A \in \mathbb{R}^{m,n}$, $P = \{ x\in \mathbb{R}^n \mid A x \leq b\}$ where $Ax \leq b$ is meant as $a_i^T x \leq b$. An alternative charakterization would be $P = \cap_{H \text{ is hyperplane}} H_{+}$, where $H_{+}$ is the half-room $\{x \in \mathbb{R}^n \mid \langle x, u \rangle \geq b\}$. ADDED convex