I have a polyhedron which is defined by the following system of inequalities:
$$ \left\{ \begin{array}{c} x \geq 0 \\ y \geq 0 \\ x + y + z \leq 2\\ x + y + 2z \geq 2 \end{array} \right. $$ The task is to find its vertices, edges and faces. Undoubtedly, I can draw a plot and solve it theoretically. The question is - how to do it analytically? In this case I am just feeling lucky because it is easy to draw a plot, but this is clearly not the way for more difficult systems and especially for polytopes, not polyhedra.