Upper Bound on the Number of Vertices of Polyhedra with $0,1$-Constraint   Matrices
  In this note we show that the maximum number of vertices in any polyhedron $P=\{x\in \mathbb{R}^d : Ax\leq b\}$ with $0,1$-constraint matrix $A$ and a real vector $b$ is at most $d!$. 
Khaled Elbassioni, Zvi Lotker, Raimund Seidel