A polyhedron is defined as the intersection of a finite collection of generalized halfspaces. In my book, a generalized halfspace is defined as a set where we allow the vector of coefficients $(a_1, a_2,\ldots, a_n )$ in the definition of a halfspace to vanish (or = 0).
I said yes. $\mathbb{R}^n$ is a polyhedron because a generalized halfspace can be all of $\mathbb{R}^n$. But I feel there's something wrong with that logic. Please help. Thanks.