Consider the set $S$ in $\mathbb R^3$ defined by the inequalities:
$x+y+z \ge 1$
$-x+y+z \le 1$
$x-y+z \le 1$
$x+y-z \le 1$
How can I show that $S$ is a $3$-simplex ? (Convex hull of $3 + 1$ affinely independent points).
I've been looking over a lot of theorems in my book of convex optimization, but I've found none that could be directly applied.
How can I by inspection find these affinely independent points ?