I have a convex polyhedron given by a set of linear inequalities, for example:
$$ x_1 \geq 0,~~ x_2 \geq 0, ~~x_3\geq 0 \\ x_1+x_2\leq 1,~~ x_2+x_3\leq 1,~~ x_3+x_1\leq 1 $$ I want to list all the extreme points of the polyhedron. In this case, these points would be: $$(0,0,0),~~(1,0,0),~~(0,1,0),~~(0,0,1),~~(1/2,1/2,1/2)$$
In python, there are several linear programming libraries, such as scipy.linprog or cvxpy, that can return one such extreme point using the Simplex method. But I want to list all of them. How can I do this?