title: Polytope, Python - find extreme points
body: <p>I need to find a list of all the extreme points of a polytope given by a matrix relation Ax &lt;= b, with x being non-negative. I know that 100% of the time, the polytope is non degenerate.
  The first solution I used was to generate a random non negative vector and run an LP with the vector being the objective function (so basically; optimizing in a random direction). This of course has many problems: take an insane amount of time and in the end I can't be sure the solution is correct.</p>
  <p>Then I tried using the <a href="https://githubhot.com/repo/tulip-control/polytope" rel="nofollow noreferrer">polytope</a> toolbox; with the 'extreme' function. I ran it on an instance I already know well:</p>
  <pre><code>import numpy as np
  import polytope as pc
      
  A = np.array([[0,1,0,1,0], [0,0,1,0,1], [1,0,0,0,1], [0,1,1,0,0], [1,0,0,0,0]])
  K = A - A.transpose()
  C = np.vstack( (K, -np.eye(5) , [1]*5)
  
  p = pc.Polytope(C, [0]*10+[1])
  print(pc.extreme(p))
  </code></pre>
  <p>The output I expect is (.5, .5, 0, 0, 0), (0, 1/3, 1/3, 1/3, 0) and (0, 0, 0, 0, 0). However, I only get a None.
  I saw there is an <a href="https://github.com/tulip-control/polytope/blob/main/examples/randplot.py" rel="nofollow noreferrer">example</a> in the repository on the use of extreme() but I don't see what I did wrong.</p>
  <p>On a side note, if you have an other library to recommand that can solve this problem (find extremal points in polyhedras) I'd be happy to take it.</p>