Wikipedia does not provide a concise definition of "polyhedron" in $\mathbb R^n$. What is the "best" - in whatever sense - definition of this class of objects?
I am interested in a definition where there are finitely many faces whilst the polyhedron may be unbounded. This includes convex polyhedra $\mathcal P$ in $\mathbb R^n$, which can be be defined as
$ x \in \mathcal P \quad \Longleftrightarrow \quad \forall 1 \leq i \leq m : a_i^t \cdot x \leq b_i$
where $a_i, \dots, a_m, b \in \mathbb R^n$.