Question 77
Let $W$ be the hypercube $\{ (x_{1}, x_{2}, x_{3}, x_{4}) \mid 0 \leq x_{1}, x_{2}, x_{3}, x_{4} \leq 1 \}$. The intersection of $W$ and a hyperplane parallel to $x_{1}+x_{2}+x_{3}+x_{4}=0$ is a non-degenerate 3-dimensional polyhedron. What is the maximum number of faces of this polyhedron?