Let $u_1,\dots,u_n$ be linearly independent unit vectors in $\mathbb R^n$. Let $T$ be the parallepiped centred at $0$, with sides parallel to $u_i$ and side lengths $l_i$, $i=1,2,\dots,n$. My question is: is there a simple algebraic expression that describes exactly the set of all points lying in the (convex hull of) the parallepiped?
If $u_1,\dots,u_n$ are orthonormal, then this will be easy: the parallepiped is just given by the set of all $\xi\in\mathbb R^n$ that satisfies the system of equations $|u_i\cdot \xi|\leq l_i/2$.
In general, this would also be obtained by repeated direct calculation, but I wonder if there is a simple formula that does the job.
In the general case, $T=\{\xi\in\mathbb{R}^n : |v_i\cdot\xi|\leqslant l_i/2, 1\leqslant i\leqslant n\}$, where $v_i$ is the $i$-th row of $V=U^{-1}$, where $U$ is composed out of $u_i$ as columns (i.e., the element $U_{ij}$ of $U$ is the $i$-th component of $u_j$).